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  • 1
    Digitale Medien
    Digitale Medien
    Cost-effective network design for groundwater flow monitoring (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 27-41 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Groundwater monitoring networks ; Information reliability ; Information scales ; Kalman filtering in groundwater
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract The extensive use of groundwater resources has increased the need for developing cost-effective monitoring networks to provide an indication of the degree to which the subsurface environment has been affected by human activities. This study presents a cost-effective approach to the design of groundwater flow monitoring networks. The groundwater network design is formulated with two problem formats: maximizing the statistical monitoring power for specified budget constraint and minimizing monitoring cost for statistical power requirement. The statistical monitoring power constraint is introduced with an information reliability threshold value. A branch and bound technique is employed to select the optimal solution from a discrete set of possible network alternatives. The method is tested to the design of groundwater flow monitoring problem in the Pomona County, California.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01547730
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  • 2
    Digitale Medien
    Digitale Medien
    Probabilistic modeling of aerated lagoons: A comparison of methodologies (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 65-81 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Lagoons ; Ponds ; Facultative ; First-order kinetics ; Complete mixing ; Probabilistic ; Uncertainty ; Environmental ; Stochastic differential equations
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract Two stochastic models are developed to describe the BOD output (i.e. effluent) variation of facultative aerated lagoons in series. One of the models uses the uncertainty analysis (UA) technique and the other is based on the moment equation solution methodology of stochastic differential equations (SDE's). The former considers a second-order approximation of the expectation (SOAE) and a first-order approximation of the variance (FOAV). The SDE model considers that output variability is accounted for by random variations in the rate coefficient. Comparisons are provided. Calibration and verification of the two models are aciieved by using field observations from two different lagoon systems in series. The predictive performances of the two models are compared with each other and with another SDE model, presented in a previous paper, that considers input randomness. The three methods show similar predictive performances and provide good predictions of the mean and standard deviation of the lagoon effluent BOD concentrations and thus are considered as appropriate methodologies.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01547733
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  • 3
    Digitale Medien
    Digitale Medien
    Estimation of the annual maximum distribution from samples of maxima in separate seasons (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 89-103 
    Details
    ISSN: 1436-3259
    Schlagwort(e): maximum precipitation depths ; extreme-value distributions ; seasonal variation ; partial duration series ; model misspecification
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract Quantile estimates of the annual maximum distribution can be obtained by fitting theoretical distributions to the maxima in separate seasons, e.g. to the monthly maxima. In this paper, asymptotic expressions for the bias and the variance of such estimates are derived for the case that the seasonal maxima follow a Gumbel distribution. Results from these expressions are presented for a situation with no seasonal variation and for maximum precipitation depths at Uccle/Ukkel (Belgium). It is shown that the bias is often negligible and that the variance reduction by using seasonal maxima instead of just the annual maxima strongly depends on the seasonal variation in the data. A comparison is made between the asymptotic standard error of quantile estimates from monthlymaxima with those from a partial duration series. Much attention is paid to the effect of model misspecification on the resulting quantile estimates of the annual maximum distribution. The use of seasonal maxima should be viewed with caution when the upper tail of this distribution is of interest.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01543284
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  • 4
    Digitale Medien
    Digitale Medien
    Parameter identification in tidal models with uncertain boundary conditions (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 193-208 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Stochastic tidal modeling ; parameter identification ; model calibration
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract In this paper a parameter estimation algorithm is developed to estimate uncertain parameters in two dimensional shallow water flow models. Since in practice the open boundary conditions of these models are usually not known accurately, the uncertainty of these boundary conditions has to be taken into account to prevent that boundary errors are interpreted by the estimation procedure as parameter fluctuations. Therefore the open boundary conditions are embedded into a stochastic environment and a constant gain extended Kalman filter is employed to identify the state of the system. Defining a error functional that measures the differences between the filtered state of the system and the measurements, a quasi Newton method is employed to determine the minimum of this functional. To reduce the computational burden, the gradient of the criterium that is required using the quasi Newton method is determined by solving the adjoint system.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01543083
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  • 5
    Digitale Medien
    Digitale Medien
    On the distribution of flood volume in partial duration series analysis of flood phenomena (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 217-226 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Exponential distribution ; bivariate exponential distribution ; distribution of flood volume ; partial duration series
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract A methodology based on the theory of stochastic processes is applied to the analysis of floods. The approach will be based on some results of the theory of extreme values over a threshold. In this paper, we focus on the estimation of the distribution of the flood volume in partial duration series analysis of flood phenomena, by using a bivariate exponential distribution of discharge exceedances and durations over a base level.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01543085
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  • 6
    Digitale Medien
    Digitale Medien
    Editorial note (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 254-254 
    Details
    ISSN: 1436-3259
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01544080
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  • 7
    Digitale Medien
    Digitale Medien
    Rehabilitation and replacement of water distribution system components considering uncertainties (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 277-294 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Water distribution ; optimization ; nonlinear programming ; integer programming ; chance constraints ; rehabilation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract This paper presents the mathematical development of an integer — nonlinear programming chance — constrained optimization model for the minimum cost rehabilitation/replacement of water distribution system components. Particular attention is given to the handling of uncertainties in the roughness factors and the loading conditions including both the random demand and preassure head requirements. The advantages of the proposed model include the ability to: 1) handle the optimal timing of rehabilitation/replacement for water distribution system components; 2) link a mixed-integer linear program solver, a nonlinear program solver, and a hydraulic simulator into an optimization framework; 3) handle the uncertainties of some of the variables; 4) incorporate various kinds of cost functions; and 5) handle multiple loading conditions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01544082
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  • 8
    Digitale Medien
    Digitale Medien
    Assessment of reliability in water distribution networks using entropy based measures (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 309-320 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Entropy ; reliability ; redundancy ; water distribution networks ; nodal pair reliability
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract Entropy based expressions for measurement of reliability and redundancy have recently been reported. These measures approach assessment of the reliability of the distribution network from the intrinsic redundancy of the network layout. The paper extends earlier work on entropy functions by including a more explicit statement of the alternate paths available in the network and by recognizing that under certain circumstances, e.g., failure of some part of the network work, an outflow link from a node under normal working condition may become an inflow link to the same node. The measures are assessed by comparison with parameters measuring Nodal Pair Reliability and percentage of flow supplied at adequate pressure for a range of networks and link failure conditions in this networks. The entropy measures are shown to reflect changes in the network reliability, as measured by these two comparative parameters, very well.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01544084
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  • 9
    Digitale Medien
    Digitale Medien
    Evaluation of risk concepts in partial duration series (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 1-16 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Partial duration series ; unbiased risk ; Bayesian risk
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract Conventional design practice aims at obtaining optimal estimates of floods with specified exceedance probabilities. Such estimates are, however, known on the average to be exceeded more frequently than expected. Alternatively, methods focusing on the expected exceedance probability can be used. Two different methods are considered here; the first is based on the sample distribution of true exceedance probabilities. The second is a Bayesian analogue using the likelihood function and a noninformative prior to describe the variability of exceedance probabilities. Appropriate analytical solutions are presented in both cases using the partial duration series approach.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01544174
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  • 10
    Digitale Medien
    Digitale Medien
    Derivation of bivariate probability density functions with exponential marginals (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 55-68 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Bivariate probability distribution ; random variables ; zero marginals ; Finch-Groblicki method
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract A vivariate probability density function (pdf),f(x 1,x 2), admissible for two random variables (X 1,X 2), is of the form $$f(x_1 x_2 ) = f_1 (x_1 )f_2 (x_2 )[1 + \rho \{ F_1 (x_1 ),F_2 (x_2 )\} ]$$ where ρ(u, v) (u=F 1(x 1),v=F 2(x 2)) is any function on the unit square that is 0-marginal and bounded below by−1 andF 1(x 1) andF 2(x 2) are cumulative distribution functions (cdf) of marginal probability density functionsf 1(x 1) andf 2(x 2). The purpose of this study is to determinef(x 1,x 2) for different forms of ρ(u,v). By considering the rainfall intensity and the corresponding depths as dependent random variables, observed and computed probability distributionsF 1(x 1),F(x 1/x 2),F 2(x 2), andF(x 2/x 1) are compared for various forms of ρ(u,v). Subsequently, the best form of ρ(u,v) is specified.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01544178
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  • 11
    Digitale Medien
    Digitale Medien
    Entropy estimation of hydrological extremes (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 77-87 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Flood ; random ; distribution ; estimation ; probability ; entropy ; fractile constraints
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract The method of Relative Entropy with Fractile constraints (REF method) is explained and applied to model extreme compound hydrological phenomena, such as extreme sea levels under storm conditions. Also presented is a simple method of Tail Entropy Approximation (TEA), which amounts to a correction of traditional statistical estimates for extreme observations. Distribution assumptions are necessary but downplayed in the REF method, relegating the prior distribution to the role of an extrapolation function. The estimates are objective in an information-theoretical sense. They also satisfy a strict requirement of self-consistency that is generally not satisfied by standard statistical methods: invariance under monotonic transformations of the random variable. Historical records of storm surge levels in the Netherlands and annual maximum tidal heights for Sheerness, UK, are used as examples. Comparison is made with distributions obtained using other methods. It is concluded that the tail entropy approximation provides simple, objective estimates of extremes in the tail beyond the range of observations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01544180
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  • 12
    Digitale Medien
    Digitale Medien
    On the use of Empirical Orthogonal Function (EOF) analysis in the simulation of random fields (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 125-134 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Empirical Orthogonal Function analysis ; random fields ; simulation ; non-homogeneous fields
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract In several fields of Geophysics, such as Hydrology, Meteorology or Oceanography, it is often useful to generate random fields, displaying the same variabilitity as the observed variables. Usually, these synthetic data are used as forcing fields into numerical models, to test the sensitivity of their outputs to the variability of the inputs. Examples can be found in subsurface or surface Hydrology and in Meteorology with General Circulation Models (GCM). Different techniques have already been proposed, often based on the spectral representation of the random process, with, usually, assumptions of stationarity. This paper suggests that Empirical Orthogonal Function (EOF) analysis, which leads to the decomposition of the covariance kernel on the set of its eigen-functions, is a possible answer to this problem. The convergence and accuracy of the method are shown to depend mainly on the number of EOFs retained in the expansion of the covariance kemel. This result is confirmed by a comparison with the turning band method and a matrix technique. Furthermore, a synthetic example of non-homogencous fields shows the interest of EOF analysis in the direct simulation of such fields.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01543054
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  • 13
    Digitale Medien
    Digitale Medien
    A univariate model for long-term streamflow forecasting (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 173-188 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Entropy ; spectral analysis ; streamflow forecasting ; univariate model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract This paper, the first in a series of two, employs the principle of maximum entropy (POME) via maximum entropy spectral analysis (MESA) to develop a univariate model for long-term streamflow forecasting. Three cases of streamflow forecasting are investigated: forward forecasting, backward forecasting (or reconstruction) and intermittent forecasting (or filling in missing records). Application of the model is discussed in the second paper.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01544056
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  • 14
    Digitale Medien
    Digitale Medien
    Modeling kinetic non-equilibrium using the first two moments of the residence time distribution (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 155-171 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Kinetic non-equilibrium ; residence time ; spatially variable chemical reactions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract A method for simulating field scale transport of kinetically adsorbing solutes is described. The non-equilibrium adsorption is modeled as a birth and death process and is coupled with the particle tracking approach using the first two moments of the distribution of the particle residence time, i.e., the time that a solute particle stays in the liquid phase. A single residence time distribution, regardless of the initial and final phase, is demonstrated to yield an accurate description of chemical kinetics in the vast majority of field scale problems. The first two moments of the residence time distribution are derived as a function of chemical reaction rates and the transport time interval Δt. It is shown that the first moment of the residence time represents a measure of the speed of the chemical reaction relative to the transport time scale Δt which is chosen depending on the velocity field. The second moment of the residence time reflects the relative importance of the chemical kinetics versus local equilibrium conditions for the given transport time step Δt. The simulated spatial moments of the contaminant plume are compared in the one-dimensional case with available analytical solutions to demonstrate the accuracy of the proposed technique. A two-dimensional case for stratified formations is presented to study the transport behavior for heterogeneous velocity fields and variable distribution coefficient, hypothesized as being negatively correlated with hydraulic conductivity. The results show that the enhanced plume spreading and the statistics of the arrival time distribution appear to be more sensitive to the spatially variable distribution coefficient than to the kinetics alone. In fact, the second spatial moment was almost doubled in the case of spatially variable distribution coefficient.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01543057
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  • 15
    Digitale Medien
    Digitale Medien
    Stochastic partial differential equations in groundwater hydrology (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 239-251 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Parameter estimation ; maximum likelihood estimation ; stochastic partial differential equation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract Part I of this series of two papers (Unny, 1989) dealt with the theoretical derivation of the moment equations for the stochastic partial differential equation in the water table depth forced by stochastic rainfall input. Part I also developed a maximum likelihood estimation procedure for parameter determination. The primary aim of the present manuscript is the application of the parameter estimation procedure to the Borden aquifer, an aquifer designated as an experimental site, where extensive field measurements have been carried out. Estimates of hydraulic conductivity and transmissivity for the Borden aquifer, derived from the maximum likelihood algorithm, have been compared with estimates obtained by “traditional” procedures. The paper also presents the simulated solution of the governing differential equation in the one dimensional problem applied to the Borden aquifer.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01544060
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  • 16
    Digitale Medien
    Digitale Medien
    Technical reports (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 280-294 
    Details
    ISSN: 1436-3259
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01543136
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  • 17
    Digitale Medien
    Digitale Medien
    Drought monitoring (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 261-266 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Drought ; drought indices
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract Drought detection, monitoring and indices are closely related to its definition. The specific definition chosen for a particular drought analysis will affect the procedures one uses in drought detection and monitoring. The traditional Palmer Drought Severity Index (PDSI) has been proven to be ineffective in regions of predominantly irrigated agriculture. The recently developed ALERT (Automated Local Evaluation in Real Time) system is proposed for use in monitoring the spatial and temporal variations of drought in real time. The ALERT system uses standardized instruments, radio frequencies, software and hardware. It was originally developed as a flash flood waming system by local flood control districts and the National Weather Service. However, now it has expanded to over 100 other uses in the areas of natural and man-made disaster detection and warning. The successful ALERT system indicates the need for the continued development of a national drought monitoring index that is applicable to a wide range of climate, hydrologic and water resource environments.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01543134
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  • 18
    Digitale Medien
    Digitale Medien
    In memory of Professor T. E. Unny (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 1-2 
    Details
    ISSN: 1436-3259
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581670
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  • 19
    Digitale Medien
    Digitale Medien
    On the control of an infinite capacity storage system (1993)
    Springer
    Stochastic environmental research and risk assessment 7 (1993), S. 195-204 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Infinite dam ; resolvent operator ; Lévy process ; integrated Markov chain
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract We consider an infinite-capacity storage system. The cumulative input to the system is assumed to be either (a) a non-decreasing Lévy process or (b) an integrated continuous-time Markov chain. Reward accumulates at a rate depending on the instantaneous release rate. The objective is to choose the release rule in such a way as to maximize the expected total discounted return. In this note we show how to determine the expected discounted return when the release rate is either constant or a linear function of the content.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585598
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  • 20
    Digitale Medien
    Digitale Medien
    Stochastic perturbation analysis of groundwater flow. Spatially variable soils, semi-infinite domains and large fluctuations (1993)
    Springer
    Stochastic environmental research and risk assessment 7 (1993), S. 213-239 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Stochastic hydrology ; perturbation ; random fields ; graph theory
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract As is well known, a complete stochastic solution of the stochastic differential equation governing saturated groundwater flow leads to an infinite hierarchy of equations in terms of higher-order moments. Perturbation techniques are commonly used to close this hierarchy, using power-series expansions. These methods are applied by truncating the series after a finite number of terms, and products of random gradients of conductivity and head potential are neglected. Uncertainty regarding the number or terms required to yield a sufficiently accurate result is a significant drawback with the application of power series-based perturbation methods for such problems. Low-order series truncation may be incapable of representing fundamental characteristics of flow and can lead to physically unreasonable and inaccurate solutions of the stochastic flow equation. To support this argument, one-dimensional, steady-state, saturated groundwater flow is examined, for the case of a spatially distributed hydraulic conductivity field. An ordinary power-series perturbation method is used to approximate the mean head, using second-order statistics to characterize the conductivity field. Then an interactive perturbation approach is introduced, which yields improved results compared to low-order, power-series perturbation methods for situations where strong interactions exist between terms in such approximations. The interactive perturbation concept is further developed using Feynman-type diagrams and graph theory, which reduce the original stochastic flow problem to a closed set of equations for the mean and the covariance functions. Both theoretical and practical advantages of diagrammatic solutions are discussed; these include the study of bounded domains and large fluctuations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585600
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  • 21
    Digitale Medien
    Digitale Medien
    Operator and integro-differential representations of conditional and unconditional stochastic subsurface flow (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 157-172 
    Details
    ISSN: 1436-3259
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract Operator representations of stochastic subsurface flow equations allow writing their solutions implicitly or explicitly in terms of integro-differential expressions. Most of these representations involve Neumann series that must be truncated or otherwise approximated to become operational. It is often claimed that truncated Neumann series allow solving groundwater flow problems in the presence of arbitrarily large heterogeneities. Such claims have so far not been backed by convincing computational examples, and we present an analysis which suggests that they may not be justified on theoretical grounds. We describe an alternative operator representation due to Neuman and Orr (1993) which avoids the use of Neumann series yet accomplishes a similar purpose. It leads to a compact integro-differential form which provides considerable new insight into the nature of the solution. When written in terms of conditional moments, our new representation contains local and nonlocal effective parameters that depend on scale and information. As such, these parameters are not unique material properties but may change as more is learned about the flow system.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01589896
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  • 22
    Digitale Medien
    Digitale Medien
    Groundwater contaminant transport including adsorption and first order decay (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 185-205 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Contaminant transport ; adsorption ; decay ; random walk ; killing ; Kolmogorov equations ; contamination of a well
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract This study deals with the transport of a contaminant in groundwater. The contaminant is subject to first order decay or linear adsorption. Its displacement can be modeled by a random walk process in which particles are killed at exponentially distributed times. Dirichlet problems are derived for the rate and mean time at which contaminated particles reach a particular part of the boundary of a certain domain. These Dirichlet problems are solved asymptotically for two types of 2D-flow patterns: flow parallel to the boundary of a domain and arbitrary flow towards a well in an aquifer.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01587234
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  • 23
    Digitale Medien
    Digitale Medien
    Nonequilibrium statistical mechanical derivation of a nonlocal Darcy's Law for unsaturated/saturated flow (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 109-116 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Unsaturated ; nonlocal ; memory ; statistical physics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract As illustrated variously by wetting and drying scanning curves, flow in unsaturated porous media is inherently nonlocal. This nonlocality is also manifest in hysteresis in the classical Darcy conductivity. It is the authors' belief that most current theories of unsaturated/saturated flow are often inadequate, as they do not account for spatial nonlocality and memory. Here we provide a fundamental theory in which nonlocality of the flow constitutive theory is a natural consequence of force balances. The results are derived from general principles in statistical physics and under appropriate limiting conditions, the classical Darcy's Law is recovered for saturated flow. A notable departure in this theory from other nonlocal flow theories is that a classical Darcy type equation on a small scale need not exist.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01589892
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  • 24
    Digitale Medien
    Digitale Medien
    Inverse methods for subsurface flow: A critical review of stochastic techniques (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 1-26 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Inverse ; calibration ; estimation ; groundwater flow
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract The development of stochastic methods for groundwater flow representation has undergone enormous expansion in recent years. The calibration of groundwater models, the inverse problem, has lately received comparable attention especially and almost exclusively from the stochastic perspective. In this review we trace the evolution of the methods to date with a specific view toward identifying the most important issues involved in the usefulness of the approaches. The methods are critiqued regarding practical usefulness, and future directions for requisite study are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01547729
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  • 25
    Digitale Medien
    Digitale Medien
    Bayes estimate of the probability of exceedance of annual floods (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 55-64 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Predictive distribution ; Bayesian approximation ; parameter uncertainty ; non-informative prior ; method of moments ; Gumbel distribution ; maximum likelihood estimates
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract In this paper Lindley's Bayesian approximation procedure is used to obtain the Bayes estimate of the probability of exceedence of a flood discharge. The Bayes estimates of the probability of exceedence has been shown by S.K. Sinha to be equivalent to the estimate of the probability of exceedence from the predictive or Bayesian disribution, of a future flood discharge. The evaluation of complex ratios of multiple integrals common in a Bayesian analysis is not necessary using Lindley's procedure. The Bayes estimates are compared to those obtained by the method of maximum likelihood and the method of moments. The results show that Bayes estimates of the probability of exceedence are larger as expected, but have smaller posterior standard deviations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01547732
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  • 26
    Digitale Medien
    Digitale Medien
    Identification of wind stress on shallow water surfaces by optimal smoothing (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 105-119 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Kalman filtering ; Optimal smoothing ; Shallow water equations ; Wind stress ; On-line prediction
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract Using the state space approach, an on-line filter procedure for combined wind stress identification and tidal flow forecasting is developed. The stochastic dynamic approach is based on the linear twodimensional shallow water equations. Using a finite difference scheme, a system representation of the model is obtained. To account for uncertainties, the system is embedded into a stochastic environment. By employing a Kalman filter, the on-line measurements of the water-level available can be used to identify and predict the shallow water flow. Because it takes a certain time before a fluctuation in the wind stress can be noticed in the water-level measurements, an optimal fixed-lag smoother is used to identify the stress.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01543285
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  • 27
    Digitale Medien
    Digitale Medien
    Advanced use into rainfall prediction of three-dimensionally scanning radar (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 135-150 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Radar ; rainfall prediction ; real-time prediction
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract A computational method for the determination of rainfall distribution for applications in short term rainfall prediction is presented here. The method is strongly influenced by the experience gained from the observation and analysis of data gathered on a heavy rainfall event in 1986 that occurred during the Baiu Season in Japan. The method is based on the concept that rainfall occurs as an interaction between an instability field, appropriately modeled, and a field of water vapor under the influence of topography. The results from this computational method showed good agreement with the temporal variation in the rainband that moved across the observation field in 1986. Towards determination of the parameters in the computational model, another method for the determination of the rainfield is also developed. This second method determines the rainfall distribution from estimation of the conversion rate of water vapor to liquid water through use of data from a three dimensional scanning radar. The results are consistent with those obtained from the first method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01543287
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  • 28
    Digitale Medien
    Digitale Medien
    Development of the instantaneous unit hydrograph using stochastic differential equations (1990)
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 151-160 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Instantaneous Unit Hydrograph ; Conceptual models ; Stochastic differential equations
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract Recognizing that simple watershed conceptual models such as the Nash cascade ofn equal linear reservoirs continue to be reasonable means to approximate the Instantaneous Unit Hydrograph (IUH), it is natural to accept that random errors generated by climatological variability of data used in fitting an imprecise conceptual model will produce an IUH which is random itself. It is desirable to define the random properties of the IUH in a watershed in order to have a more realistic hydrologic application of this important function. Since in this case the IUH results from a series of differential equations where one or more of the uncertain parameters is treated in stochastic terms, then the statistical properties of the IUH are best described by the solution of the corresponding Stochastic Differential Equations (SDE's). This article attempts to present a methodology to derive the IUH in a small watershed by combining a classical conceptual model with the theory of SDE's. The procedure is illustrated with the application to the Middle Thames River, Ontario, Canada, and the model is verified by the comparison of the simulated statistical measures of the IUH with the corresponding observed ones with good agreement.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01543288
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  • 29
    Digitale Medien
    Digitale Medien
    An exact solution of solute transport by one-dimensional random velocity fields (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 45-54 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Solute transport ; random velocity ; Lagrangian description ; travel time ; nonlinear effects
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract The problem of one-dimensional transport of passive solute by a random steady velocity field is investigated. This problem is representative of solute movement in porous media, for example, in vertical flow through a horizontally stratified formation of variable porosity with a constant flux at the soil surface. Relating moments of particle travel time and displacement, exact expressions for the advection and dispersion coefficients in the Focker-Planck equation are compared with the perturbation results for large distances. The first- and second-order approximations for the dispersion coefficient are robust for a lognormal velocity field. The mean Lagrangian velocity is the harmonic mean of the Eulerian velocity for large distances. This is an artifact of one-dimensional flow where the continuity equation provides for a divergence free fluid flux, rather than a divergence free fluid velocity.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01544177
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  • 30
    Digitale Medien
    Digitale Medien
    Stochastic overland flows (1991)
    Springer
    Stochastic environmental research and risk assessment 5 (1991), S. 89-104 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Overland flows ; nonlinear SPDE ; evolutionary probability distributions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract A theoretical solution framework to the nonlinear stochastic partial differential equations (SPDE) of the kinematic wave and diffusion wave models of overland flows under stochastic inflows/outflows, stochastic surface roughness field and stochastic state of flows was obtained. This development was realized by means of an eigenfunction representation of the time-space overland flow depths, and by transforming the problem into the phase space. By using Van Kampen's lemma and the cumulant expansion theory of Kubo-Van Kampen-Fox, the deterministic partial differential equation (PDE) for the evolutionary probability density function (pdf) of overland flow depths was finally obtained. Once this deterministic PDE is solved for the time-varying pdf of overland flow depths, then the time-space varying pdf of overland flow depths can be obtained by a transformation given in the text. In this solution framework it is possible to incorporate the stochastic dynamic behavior of the parameters and of the forcing functions of the overland flow process. For example, not only the individual rainfall duration and fluctuating rain intensity characteristics but also the sequential behavior of rainfall patterns is incorporated into the evolutionary probability density function of overland flow depths.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01543052
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  • 31
    Digitale Medien
    Digitale Medien
    Analysis of macrodispersion through volume-averaging: Moment equations (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 5-25 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Solute transport ; Heterogeneity ; Dispersion
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract Macrodispersion is spreading of a substance induced by spatial variations in local advective velocity at field scales. Consider the case that the steady-state seepage velocity and the local dispersion coefficients in a heterogeneous formation may be modeled as periodic in all directions in an unbounded domain. The equations satisfied by the first two spatial moments of the concentration are derived for the case of a conservative non-reacting solute. It is shown that the moments can be calculated from the solution of well-defined deterministic boundary value problems. Then, it is described how the rate of increase of the first two moments can be calculated at large times using a Taylor-Aris analysis as generalized by Brenner. It is demonstrated that the second-order tensor of macrodispersion (or effective dispersion) can be computed through the solution of steady-state boundary-value problems followed by the determination of volume averages. The analysis is based solely on volume averaging and is not limited by the assumption that the fluctuations are small. The large-time results are valid when the system is in a form of equilibrium in which a tagged particle samples all locations in an appropriately defined “phase space” with equal probability.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581672
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  • 32
    Digitale Medien
    Digitale Medien
    A theory of efficiency of storage-treatment systems (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 89-101 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Detention storage ; Pollution control ; Non-point pollutant runoff
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract A simple expression is presented on the capability of storage-treatment systems to reduce non-point pollutant runoff load to natural waters. Their efficiency depends on the capacities of the facilities and probabilistic properties of runoff, such as interval, duration, volume, and concentration of runoff events. Assuming the compound Poisson process for runoff time series, the exact expressions of the ratio of treated load in terms of storage and treatment capacities are theoretically derived on the neighbourhoods of all boundaries of the domain on which the problem is defined. Then, an approximate expression over the whole domain is presented, of which the value and the first-order derivative coincide with those of the exact derived expressions near the boundaries. Accuracy is checked by Monte Carlo simulations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01591332
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  • 33
    Digitale Medien
    Digitale Medien
    On the generation of drought events using an alternating renewal-reward model (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 55-68 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Drought severity ; Drought duration ; Renewal-reward process
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract This research study focused on the hypothesis that extreme drought and high streamflow events come from different independent populations with different probability distributions which need to be studied separately, rather than considering the streamflow population as a whole. The inability of traditional streamflow generator models to consistently reproduce the frequency of occurrence of severe droughts observed in the historical record has been questioned by many researchers. Our study focused on the development of astochastic event generator model which would be capable of doing so. This was accomplished in a two-step process by first generating the drought event, and then deriving the streamflows which comprised that event. The model considered for this analysis was an alternating renewal-reward procedure that cycles between eventon andoff times, and is representative of drought or high streamflow event duration. The reward gained while the event ison oroff represents drought severity or high streamflow surplus. Geometric and gamma distributions were considered for drought duration and deficit respectively. Model validation was performed using calculated required capacities from the sequent peak algorithm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581675
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  • 34
    Digitale Medien
    Digitale Medien
    Probabilistic sensitivity and modeling of two-dimensional transport in porous media (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 103-121 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Probabilistic model ; Sensitivity ; Contaminant transport
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract A reliability approach is used to develop a probabilistic model of two-dimensional non-reactive and reactive contaminant transport in porous media. The reliability approach provides two important quantitative results: an estimate of the probability that contaminant concentration is exceeded at some location and time, and measures of the sensitivity of the probabilistic outcome to likely changes in the uncertain variables. The method requires that each uncertain variable be assigned at least a mean and variance; in this work we also incorporate and investigate the influence of marginal probability distributions. Uncertain variables includex andy components of average groundwater flow velocity,x andy components of dispersivity, diffusion coefficient, distribution coefficient, porosity and bulk density. The objective is to examine the relative importance of each uncertain variable, the marginal distribution assigned to each variable, and possible correlation between the variables. Results utilizing a two-dimensional analytical solution indicate that the probabilistic outcome is generally very sensitive to likely changes in the uncertain flow velocity. Uncertainty associated with dispersivity and diffusion coefficient is often not a significant issue with respect to the probabilistic analysis; therefore, dispersivity and diffusion coefficient can often be treated for practical analysis as deterministic constants. The probabilistic outcome is sensitive to the uncertainty of the reaction terms for early times in the flow event. At later times, when source contaminants are released at constant rate throughout the study period, the probabilistic outcome may not be sensitive to changes in the reaction terms. These results, although limited at present by assumptions and conceptual restrictions inherent to the closed-form analytical solution, provide insight into the critical issues to consider in a probabilistic analysis of contaminant transport. Such information concerning the most important uncertain parameters can be used to guide field and laboratory investigations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01591333
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  • 35
    Digitale Medien
    Digitale Medien
    Contamination of a well in a uniform background flow (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 191-207 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Hydrodynamic dispersion ; Fokker-Planck equation ; backward equation ; boundary layer ; complex potential function ; fraction of contaminated particles that enter a well
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract In this paper we describe the transport of pollution in groundwater in the neighbourhood of a well in a uniform background flow. We compute the rate at which contaminated particles reach the well as a function of the place of the source of pollution. The motion of a particle in a dispersive flow is seen as a random walk process. The Fokker-Planck equation for the random motion of a particle is transformed using the complex potential for the advective flow field. The resulting equation is solved asymptotically after a stretching transformation. Finally, the analytical solution is compared with results from Monte Carlo simulations with the random walk model. The method can be extended to arbitrary flow fields. Then by a numerical coordinate transformation the analytical results can still be employed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581450
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  • 36
    Digitale Medien
    Digitale Medien
    Generation of runoff series at ungauged locations using empirical orthogonal functions in combination with kriging (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 255-269 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Emprical Orthogonal Functions ; interpolating runoff ; kriging
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract The method of Empirical Orthogonal Functions (EOF method) is combined with an objective interpolation technique, kriging, to generate runoff series at ungauged locations. In a case study the results are compared to series interpolated by a combination of EOF analysis and regression using catchment characteristics as independent variables. The results are also compared to linear weighting of an existing runoff series, a commonly used method for spatial interpolation. The influence of altitude on the runoff is studied comparing kriging based on 2 and 3 coordinates. The study showed that the capacity of EOF analysis combined with kriging is as good as the traditionally used linear weighting. The results, when altitude is included in the kriging, are improved.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581620
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  • 37
    Digitale Medien
    Digitale Medien
    Estimation of periodicities in hydrologic data (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 270-288 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Periodicities ; hydraulic cycle ; spectral methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract Periodicites in hydrologic data are frequently estimated and studied. In some cases the periodic components are subtracted from the data to obtain the stochastic components. In other cases the physical reasons for the occurrence of these periodicities are investigated. Apart from the annual cycle in the hydrologic data, periods corresponding to the 11 year sunspot cycle, the Hale cycle and others have been detected. The conclusions from most of these studies depend on the reliability and robustness of the methods used to detect these periodicities. Several spectral analysis methods have been proposed to investigate periodicities in time series data. Several of these have been compared to each other. The methods by Siddiqui and Wang and by Damsleth and Spjotvoll, which are stepwise procedures of spectrum estimation, have not been evaluated. Two of the methods of spectral analysis proposed by Siddiqui and Wang and by Damsleth and Spjotvoll are investigated in this study by using generated and observed data. Siddiqui and Wang's method is found to be superior to the Damsleth and Spjotvoll's method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581621
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  • 38
    Digitale Medien
    Digitale Medien
    On the shot-noise streamflow model and its applications (1992)
    Springer
    Stochastic environmental research and risk assessment 6 (1992), S. 289-303 
    Details
    ISSN: 1436-3259
    Schlagwort(e): Stream flow series ; shot-noise model ; sadolle-point approximation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Architektur, Bauingenieurwesen, Vermessung , Energietechnik , Geographie , Geologie und Paläontologie
    Notizen: Abstract In this paper we consider the shot-noise model of streamflow series. We show how design discharge can be obtained by the stochastic intensity of thinned Poisson processes describing the peaks over a threshold. The main result concerns the stationary distribution of peaks. We derive an explicit expression for this limit distribution in terms of its Laplace transform. Approximation formulas are developed making use of the saddle point method for the asymptotic evaluation of contour integrals and the Post-Widder formula for inversion of Laplace transforms. We illustrate this methods on the case of Gamma-distributed shots. The stationary peak distribution is used to approximate the maximum value distribution for larger time intervals.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581622
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  • 39
    Digitale Medien
    Digitale Medien
    Optimizing over the subtour polytope of the travelling salesman problem (1990)
    Springer
    Mathematical programming 49 (1990), S. 163-187 
    Details
    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract A commonly studied relaxation of the travelling salesman problem is obtained by adding subtour elimination constraints to the constraints of a 2-factor problem and removing the integrality requirement. We investigate the problem of solving this relaxation for a special type of objective function. We also discuss some ways in which this relates to the concept of rank introduced by Chvátal.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588786
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  • 40
    Digitale Medien
    Digitale Medien
    Concurrent stochastic methods for global optimization (1990)
    Springer
    Mathematical programming 46 (1990), S. 1-29 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Global optimization ; concurrent ; parallel ; stochastic ; network of computers
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The global optimization problem, finding the lowest minimizer of a nonlinear function of several variables that has multiple local minimizers, appears well suited to concurrent computation. This paper presents a new parallel algorithm for the global optimization problem. The algorithm is a stochastic method related to the multi-level single-linkage methods of Rinnooy Kan and Timmer for sequential computers. Concurrency is achieved by partitioning the work of each of the three main parts of the algorithm, sampling, local minimization start point selection, and multiple local minimizations, among the processors. This parallelism is of a coarse grain type and is especially well suited to a local memory multiprocessing environment. The paper presents test results of a distributed implementation of this algorithm on a local area network of computer workstations. It also summarizes the theoretical properties of the algorithm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585724
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  • 41
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    Digitale Medien
    Proximity control in bundle methods for convex nondifferentiable minimization (1990)
    Springer
    Mathematical programming 46 (1990), S. 105-122 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nondifferentiable minimization ; convex programming ; numerical methods ; descent methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Proximal bundle methods for minimizing a convex functionf generate a sequence {x k } by takingx k+1 to be the minimizer of $$\hat f^k (x) + u^k |x - x^k |^2 /2$$ , where $$\hat f^k $$ is a sufficiently accurate polyhedral approximation tof andu k 〉 0. The usual choice ofu k = 1 may yield very slow convergence. A technique is given for choosing {u k } adaptively that eliminates sensitivity to objective scaling. Some encouraging numerical experience is reported.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585731
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  • 42
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    Digitale Medien
    Relaxation methods for monotropic programs (1990)
    Springer
    Mathematical programming 46 (1990), S. 127-151 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Dual descent ; monotropic program ; Tucker tableau ; elementary vector
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We propose a dual descent method for the problem of minimizing a convex, possibly nondifferentiable, separable cost subject to linear constraints. The method has properties reminiscent of the Gauss-Seidel method in numerical analysis and uses theε-complementary slackness mechanism introduced in Bertsekas, Hosein and Tseng (1987) to ensure finite convergence to near optimality. As special cases we obtain the methods in Bertsekas, Hosein and Tseng (1987) for network flow programs and the methods in Tseng and Bertsekas (1987) for linear programs.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585734
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  • 43
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    Digitale Medien
    Algebraic optimization: The Fermat-Weber location problem (1990)
    Springer
    Mathematical programming 46 (1990), S. 219-224 
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    ISSN: 1436-4646
    Schlagwort(e): Algebraic optimization ; location theory ; ellipsoid algorithms
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The Fermat-Weber location problem is to find a point in ℝ n that minimizes the sum of the (weighted) Euclidean distances fromm given points in ℝ n . In this work we discuss some relevant complexity and algorithmic issues. First, using Tarski's theory on solvability over real closed fields we argue that there is an infinite scheme to solve the problem, where the rate of convergence is equal to the rate of the best method to locate a real algebraic root of a one-dimensional polynomial. Secondly, we exhibit an explicit solution to the strong separation problem associated with the Fermat-Weber model. This separation result shows that anε-approximation solution can be constructed in polynomial time using the standard Ellipsoid Method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585739
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  • 44
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    Digitale Medien
    A short proof of finiteness of Murty's principal pivoting algorithm (1990)
    Springer
    Mathematical programming 46 (1990), S. 255-256 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Linear complementarity problem ; P-matrix
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We give a short proof of the finiteness of Murty's principal pivoting algorithm for solving the linear complementarity problemy = Mz + q, y T z = 0,y ≥ 0,z ≥ 0 withP-matrixM.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585743
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  • 45
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    Digitale Medien
    Convergence properties of trust region methods for linear and convex constraints (1990)
    Springer
    Mathematical programming 47 (1990), S. 305-336 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Trust region ; linear constraints ; convex constraints ; global convergence ; local convergence ; degeneracy ; rate of convergence ; identification of active constraints ; Newton's method ; sequential quadratic programming ; gradient projection
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We develop a convergence theory for convex and linearly constrained trust region methods which only requires that the step between iterates produce a sufficient reduction in the trust region subproblem. Global convergence is established for general convex constraints while the local analysis is for linearly constrained problems. The main local result establishes that if the sequence converges to a nondegenerate stationary point then the active constraints at the solution are identified in a finite number of iterations. As a consequence of the identification properties, we develop rate of convergence results by assuming that the step is a truncated Newton method. Our development is mainly geometrical; this approach allows the development of a convergence theory without any linear independence assumptions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01580867
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  • 46
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    Digitale Medien
    Active set algorithms for isotonic regression; A unifying framework (1990)
    Springer
    Mathematical programming 47 (1990), S. 425-439 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Isotonic regression ; active sets
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this and subsequent papers we will show that several algorithms for the isotonic regression problem may be viewed as active set methods. The active set approach provides a unifying framework for studying algorithms for isotonic regression, simplifies the exposition of existing algorithms and leads to several new efficient algorithms. We also investigate the computational complexity of several algorithms. In this paper we consider the isotonic regression problem with respect to a complete order $$\begin{gathered} minimize\sum\limits_{i = 1}^n {w_i } (y_i - x_i )^2 \hfill \\ subject tox_1 \leqslant x_2 \leqslant \cdot \cdot \cdot \leqslant x_n \hfill \\ \end{gathered} $$ where eachw i is strictly positive and eachy i is an arbitrary real number. We show that the Pool Adjacent Violators algorithm (due to Ayer et al., 1955; Miles, 1959; Kruskal, 1964), is a dual feasible active set method and that the Minimum Lower Set algorithm (due to Brunk et al., 1957) is a primal feasible active set method of computational complexity O(n 2). We present a new O(n) primal feasible active set algorithm. Finally we discuss Van Eeden's method and show that it is of worst-case exponential time complexity.
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    URL: http://dx.doi.org/10.1007/BF01580873
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  • 47
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    Digitale Medien
    Call for nominations for the D.R. Fulkerson Prize 1991 (1990)
    Springer
    Mathematical programming 47 (1990), S. 463-463 
    Details
    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01580877
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  • 48
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    Digitale Medien
    On multilevel iterative methods for optimization problems (1990)
    Springer
    Mathematical programming 48 (1990), S. 1-17 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Coercivity ; quadratic programming ; linear programming ; aggregation ; relaxation ; multigrid methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper is concerned with multilevel iterative methods which combine a descent scheme with a hierarchy of auxiliary problems in lower dimensional subspaces. The construction of auxiliary problems as well as applications to elasto-plastic model and linear programming are described. The auxiliary problem for the dual of a perturbed linear program is interpreted as a dual of perturbed aggregated linear program. Coercivity of the objective function over the feasible set is sufficient for the boundedness of the iterates. Equivalents of this condition are presented in special cases.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01582249
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  • 49
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    Digitale Medien
    Making sparse matrices sparser: Computational results (1990)
    Springer
    Mathematical programming 49 (1990), S. 91-111 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Sparse matrices ; linear programming ; bipartite matching
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Many optimization algorithms involve repeated processing of a fixed set of linear constraints. If we pre-process the constraint matrixA to be sparser, then algebraic operations onA will become faster. We consider the problem of making a given matrix as sparse as possible, theSparsity Problem (SP). In a companion paper with S. Frank Chang, we developed some theoretical algorithms for SP under a non-degeneracy assumption (McCormick and Chang, 1988). Here we investigate what must be done to make those algorithms applicable in practice. We report encouraging computational results in making linear programming constraint matrices sparser. We also find that the Simplex Algorithm can solve the reduced LPs faster. Comparisons are made to a heuristic algorithm for SP of Adler et al. (1989).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588780
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  • 50
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    Digitale Medien
    Deriving collinear scaling algorithms as extensions of quasi-Newton methods and the local convergence of DFP- and BFGS-related collinear scaling algorithms (1990)
    Springer
    Mathematical programming 49 (1990), S. 23-48 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Quasi-Newton methods ; collinear scalings ; conic approximations ; local and q-superlinear convergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper is concerned with collinear scaling algorithms for unconstrained minimization where the underlying local approximants are forced to interpolate the objective function value and gradient at only the two most recent iterates. By suitably modifying the procedure of Sorensen (1980) for deriving such algorithms, we show that two members of the algorithm class derived related to the DFP and BFGS methods respectively are locally and q-superlinearly convergent. This local analysis as well as the results they yield exhibit the same sort of “duality” exhibited by those of Broyden, Dennis and Moré (1973) and Dennis and Moré (1974) for the DFP and BFGS methods. The results in this paper also imply the local and q-superlinear convergence of collinear scaling algorithms of Sorensen (1982, pp. 154–156) related to the DFP and BFGS methods.
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    URL: http://dx.doi.org/10.1007/BF01588777
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  • 51
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    Digitale Medien
    OnQ-matrices (1990)
    Springer
    Mathematical programming 49 (1990), S. 139-141 
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    ISSN: 1436-4646
    Schlagwort(e): Linear complementarity problem ; copositive ; strictly copositive ; Q-matrix
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Recently, Jeter and Pye gave an example to show that Pang's conjecture, thatL 1 ⋂Q $$ \subseteq R_0 $$ , is false. We show in this article that the above conjecture is true for symmetric matrices. Specifically, we show that a symmetric copositive matrix is inQ if and only if it is strictly copositive.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588783
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  • 52
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    Digitale Medien
    Feasibility issues in a primal-dual interior-point method for linear programming (1990)
    Springer
    Mathematical programming 49 (1990), S. 145-162 
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    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; interior-point methods ; primal—dual algorithms ; feasibility
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract A new method for obtaining an initial feasible interior-point solution to a linear program is presented. This method avoids the use of a “big-M”, and is shown to work well on a standard set of test problems. Conditions are developed for obtaining a near-optimal solution that is feasible for an associated problem, and details of the computational testing are presented. Other issues related to obtaining and maintaining accurate feasible solutions to linear programs with an interior-point method are discussed. These issues are important to consider when solving problems that have no primal or dual interior-point feasible solutions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588785
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  • 53
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    Digitale Medien
    A successive quadratic programming method for a class of constrained nonsmooth optimization problems (1990)
    Springer
    Mathematical programming 49 (1990), S. 231-251 
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    ISSN: 1436-4646
    Schlagwort(e): Nonsmooth optimization ; subgradient ; ε-subgradient ; exact penalty function ; successive quadratic programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper we present an algorithm for solving nonlinear programming problems where the objective function contains a possibly nonsmooth convex term. The algorithm successively solves direction finding subproblems which are quadratic programming problems constructed by exploiting the special feature of the objective function. An exact penalty function is used to determine a step-size, once a search direction thus obtained is judged to yield a sufficient reduction in the penalty function value. The penalty parameter is adjusted to a suitable value automatically. Under appropriate assumptions, the algorithm is shown to produce an approximate optimal solution to the problem with any desirable accuracy in a finite number of iterations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588789
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  • 54
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    Digitale Medien
    An O(n 3 L) primal interior point algorithm for convex quadratic programming (1990)
    Springer
    Mathematical programming 49 (1990), S. 325-340 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Convex quadratic programming ; interior point method ; Karmarkar's method ; logarithmic barrier function method
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We present a primal interior point method for convex quadratic programming which is based upon a logarithmic barrier function approach. This approach generates a sequence of problems, each of which is approximately solved by taking a single Newton step. It is shown that the method requires $$O(\sqrt n L)$$ iterations and O(n 3.5 L) arithmetic operations. By using modified Newton steps the number of arithmetic operations required by the algorithm can be reduced to O(n 3 L).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588795
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  • 55
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    Digitale Medien
    On the equivalence between strong solvability and strict semimonotonicity for some systems involving Z-functions (1990)
    Springer
    Mathematical programming 49 (1990), S. 371-379 
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    ISSN: 1436-4646
    Schlagwort(e): Z-function ; strong solvability with nonnegativity ; strictly semimonotone function
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper focuses on the relationship between the ‘strong’ solvability of a certain system involving a Z-function, and the strict semimonotonicity of such a function. Our main result shows that, for a system defined by a continuous, superhomogeneous Z-function, the additional condition of strict semimonotonicity is both necessary and sufficient for strong solvability.
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    URL: http://dx.doi.org/10.1007/BF01588798
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  • 56
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    Digitale Medien
    On the solution of concave knapsack problems (1990)
    Springer
    Mathematical programming 49 (1990), S. 397-411 
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    ISSN: 1436-4646
    Schlagwort(e): Concave functions ; knapsack problems ; strict minimizers ; NP-hard ; nonconvex ; local minimizers
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We consider a version of the knapsack problem which gives rise to a separable concave minimization problem subject to bounds on the variables and one equality constraint. We characterize strict local miniimizers of concave minimization problems subject to linear constraints, and use this characterization to show that although the problem of determining a global minimizer of the concave knapsack problem is NP-hard, it is possible to determine a local minimizer of this problem with at most O(n logn) operations and 1+[logn] evaluations of the function. If the function is quadratic this algorithm requires at most O(n logn) operations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588800
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  • 57
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    Digitale Medien
    The graphical relaxation: A new framework for the symmetric traveling salesman polytope (1993)
    Springer
    Mathematical programming 58 (1993), S. 53-88 
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    ISSN: 1436-4646
    Schlagwort(e): Symmetric traveling salesman problem ; graphical traveling salesman problem ; polyhedron ; facet ; linear inequality ; lifting ; composition of inequalities
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract A present trend in the study of theSymmetric Traveling Salesman Polytope (STSP(n)) is to use, as a relaxation of the polytope, thegraphical relaxation (GTSP(n)) rather than the traditionalmonotone relaxation which seems to have attained its limits. In this paper, we show the very close relationship between STSP(n) and GTSP(n). In particular, we prove that every non-trivial facet of STSP(n) is the intersection ofn + 1 facets of GTSP(n),n of which are defined by the degree inequalities. This fact permits us to define a standard form for the facet-defining inequalities for STSP(n), that we calltight triangular, and to devise a proof technique that can be used to show that many known facet-defining inequalities for GTSP(n) define also facets of STSP(n). In addition, we give conditions that permit to obtain facet-defining inequalities by composition of facet-defining inequalities for STSP(n) and general lifting theorems to derive facet-defining inequalities for STSP(n +k) from inequalities defining facets of STSP(n).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581259
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  • 58
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    Digitale Medien
    Solution of linear least squares via the ABS algorithm (1993)
    Springer
    Mathematical programming 58 (1993), S. 111-136 
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    ISSN: 1436-4646
    Schlagwort(e): ABS algorithms ; linear least squares ; overdetermined linear systems ; QR factorization ; Gram–Schmidt algorithm ; numerical experiments
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The ABS class for linear and nonlinear systems has been recently introduced by Abaffy, Broyden, Galantai and Spedicato. Here we consider various ways of applying these algorithms to the determination of the minimal euclidean norm solution of over-determined linear systems in the least squares sense. Extensive numerical experiments show that the proposed algorithms are efficient and that one of them usually gives better accuracy than standard implementations of the QR orthogonalization algorithm with Householder reflections.
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    URL: http://dx.doi.org/10.1007/BF01581261
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  • 59
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    Digitale Medien
    Near boundary behavior of primal—dual potential reduction algorithms for linear programming (1993)
    Springer
    Mathematical programming 58 (1993), S. 243-255 
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    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; interior point algorithm ; primal—dual potential function
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper is concerned with selection of theρ-parameter in the primal—dual potential reduction algorithm for linear programming. Chosen from [n + $$\sqrt n $$ , ∞), the level ofρ determines the relative importance placed on the centering vs. the Newton directions. Intuitively, it would seem that as the iterate drifts away from the central path towards the boundary of the positive orthant,ρ must be set close ton + $$\sqrt n $$ . This increases the relative importance of the centering direction and thus helps to ensure polynomial convergence. In this paper, we show that this is unnecessary. We find for any iterate thatρ can be sometimes chosen in a wide range [n + $$\sqrt n $$ , ∞) while still guaranteeing the currently best convergence rate of O( $$\sqrt n $$ L) iterations. This finding is encouraging since in practice large values ofρ have resulted in fast convergence rates. Our finding partially complements the recent result of Zhang, Tapia and Dennis (1990) concerning the local convergence rate of the algorithm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581269
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  • 60
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    Digitale Medien
    A lift-and-project cutting plane algorithm for mixed 0–1 programs (1993)
    Springer
    Mathematical programming 58 (1993), S. 295-324 
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    ISSN: 1436-4646
    Schlagwort(e): Cutting planes ; projection ; mixed 0–1 programming ; disjunctive programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We propose a cutting plane algorithm for mixed 0–1 programs based on a family of polyhedra which strengthen the usual LP relaxation. We show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point. This cut is found through the solution of a linear program that has about twice the size of the usual LP relaxation. A lifting step is used to reduce the size of the LP's needed to generate the cuts. An additional strengthening step suggested by Balas and Jeroslow is then applied. We report our computational experience with a preliminary version of the algorithm. This approach is related to the work of Balas on disjunctive programming, the matrix cone relaxations of Lovász and Schrijver and the hierarchy of relaxations of Sherali and Adams.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581273
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  • 61
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    Digitale Medien
    Referees 1992 (1993)
    Springer
    Mathematical programming 58 (1993), S. 429-431 
    Details
    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581279
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  • 62
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    Digitale Medien
    Call for papers (1993)
    Springer
    Mathematical programming 58 (1993), S. 433-434 
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    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581280
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  • 63
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    Theoretical convergence of large-step primal—dual interior point algorithms for linear programming (1993)
    Springer
    Mathematical programming 59 (1993), S. 1-21 
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    ISSN: 1436-4646
    Schlagwort(e): Primal—dual interior point algorithm ; linear program ; large step ; global convergence ; polynomial-time convergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper proposes two sets of rules, Rule G and Rule P, for controlling step lengths in a generic primal—dual interior point method for solving the linear programming problem in standard form and its dual. Theoretically, Rule G ensures the global convergence, while Rule P, which is a special case of Rule G, ensures the O(nL) iteration polynomial-time computational complexity. Both rules depend only on the lengths of the steps from the current iterates in the primal and dual spaces to the respective boundaries of the primal and dual feasible regions. They rely neither on neighborhoods of the central trajectory nor on potential function. These rules allow large steps without performing any line search. Rule G is especially flexible enough for implementation in practically efficient primal—dual interior point algorithms.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581234
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  • 64
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    Digitale Medien
    Restricted simplicial decomposition for convex constrained problems (1993)
    Springer
    Mathematical programming 59 (1993), S. 71-85 
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    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The strategy of Restricted Simplicial Decomposition is extended to convex programs with convex constraints. The resulting algorithm can also be viewed as an extension of the (scaled) Topkis—Veinott method of feasible directions in which the master problem involves optimization over a simplex rather than the usual line search. Global convergence of the method is proven and conditions are given under which the master problem will be solved a finite number of times. Computational testing with dense quadratic problems confirms that the method dramatically improves the Topkis—Veinott algorithm and that it is competitive with the generalized reduced gradient method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581238
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  • 65
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    Digitale Medien
    Combining phase I and phase II in a potential reduction algorithm for linear programming (1993)
    Springer
    Mathematical programming 59 (1993), S. 133-150 
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    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; interior-point methods ; combined phase I—phase II
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper describes an affine potential reduction algorithm for linear programming that simultaneously seeks feasibility and optimality. The algorithm is closely related to a similar method of Anstreicher. The new features are that we use a two-dimensional programming problem to derive better lower bounds than Anstreicher, that our direction-finding subproblem treats phase I and phase II more symmetrically, and that we do not need an initial lower bound. Our method also allows for the generation of a feasible solution (so that phase I is terminated) during the course of the iterations, and we describe two ways to encourage this behavior.
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    URL: http://dx.doi.org/10.1007/BF01581241
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  • 66
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    A quadratically convergent O( $$\sqrt n $$ L)-iteration algorithm for linear programming (1993)
    Springer
    Mathematical programming 59 (1993), S. 151-162 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; primal and dual ; superlinear and quadratic convergence ; polynomiality
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Recently, Ye, Tapia and Zhang (1991) demonstrated that Mizuno—Todd—Ye's predictor—corrector interior-point algorithm for linear programming maintains the O( $$\sqrt n $$ L)-iteration complexity while exhibiting superlinear convergence of the duality gap to zero under the assumption that the iteration sequence converges, and quadratic convergence of the duality gap to zero under the assumption of nondegeneracy. In this paper we establish the quadratic convergence result without any assumption concerning the convergence of the iteration sequence or nondegeneracy. This surprising result, to our knowledge, is the first instance of a demonstration of polynomiality and superlinear (or quadratic) convergence for an interior-point algorithm which does not assume the convergence of the iteration sequence or nondegeneracy.
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    URL: http://dx.doi.org/10.1007/BF01581242
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  • 67
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    Digitale Medien
    The partition problem (1993)
    Springer
    Mathematical programming 59 (1993), S. 87-115 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Graph partition ; multiway cut ; polytope ; facet
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper we describe several forms of thek-partition problem and give integer programming formulations of each case. The dimension of the associated polytopes and some basic facets are identified. We also give several valid and facet defining inequalities for each of the polytopes.
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    URL: http://dx.doi.org/10.1007/BF01581239
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  • 68
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    Digitale Medien
    On the convergence of iterative methods for symmetric linear complementarity problems (1993)
    Springer
    Mathematical programming 59 (1993), S. 33-48 
    Details
    ISSN: 1436-4646
    Schlagwort(e): 90C33 ; Linear complementary problems ; iterative methods ; quadratic programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We prove convergence of the whole sequence generated by any of a large class of iterative algorithms for the symmetric linear complementarity problem (LCP), under the only hypothesis that a quadratic form associated with the LCP is bounded below on the nonnegative orthant. This hypothesis holds when the matrix is strictly copositive, and also when the matrix is copositive plus and the LCP is feasible. The proof is based upon the linear convergence rate of the sequence of functional values of the quadratic form. As a by-product, we obtain a decomposition result for copositive plus matrices. Finally, we prove that the distance from the generated sequence to the solution set (and the sequence itself, if its limit is a locally unique solution) have a linear rate of R-convergence.
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    URL: http://dx.doi.org/10.1007/BF01581236
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  • 69
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    Digitale Medien
    Effort associated with a class of random optimization methods (1991)
    Springer
    Mathematical programming 50 (1991), S. 91-98 
    Details
    ISSN: 1436-4646
    Schlagwort(e): 65K10 ; 62E15 ; 60F99 ; Random optimization ; expected length
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract When differentiability is not assumed random procedures can be successfully used to estimate the extreme values of a given function. For a class of such algorithms we treat the problem of estimating the mean effort.
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    URL: http://dx.doi.org/10.1007/BF01594927
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  • 70
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    Digitale Medien
    A note on the prize collecting traveling salesman problem (1993)
    Springer
    Mathematical programming 59 (1993), S. 413-420 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Linear programming ; prize collecting ; rounding fractional solutions ; traveling salesman problem ; worst-case analysis
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We study the version of the prize collecting traveling salesman problem, where the objective is to find a tour that visits a subset of vertices such that the length of the tour plus the sum of penalties associated with vertices not in the tour is as small as possible. We present an approximation algorithm with constant bound. The algorithm is based on Christofides' algorithm for the traveling salesman problem as well as a method to round fractional solutions of a linear programming relaxation to integers, feasible for the original problem.
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    URL: http://dx.doi.org/10.1007/BF01581256
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  • 71
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    Digitale Medien
    Limiting behavior of the affine scaling continuous trajectories for linear programming problems (1991)
    Springer
    Mathematical programming 50 (1991), S. 29-51 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Interior-point methods ; linear programming ; Karmarkar's algorithm ; logarithmic barrier function ; affine scaling algorithms ; continuous trajectories for linear programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We consider the continuous trajectories of the vector field induced by the primal affine scaling algorithm as applied to linear programming problems in standard form. By characterizing these trajectories as solutions of certain parametrized logarithmic barrier families of problems, we show that these trajectories tend to an optimal solution which in general depends on the starting point. By considering the trajectories that arise from the Lagrangian multipliers of the above mentioned logarithmic barrier families of problems, we show that the trajectories of the dual estimates associated with the affine scaling trajectories converge to the so called ‘centered’ optimal solution of the dual problem. We also present results related to asymptotic direction of the affine scaling trajectories. We briefly discuss how to apply our results to linear programs formulated in formats different from the standard form. Finally, we extend the results to the primal-dual affine scaling algorithm.
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    URL: http://dx.doi.org/10.1007/BF01594923
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  • 72
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    Convergence of a generalized subgradient method for nondifferentiable convex optimization (1991)
    Springer
    Mathematical programming 50 (1991), S. 75-80 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Subgradient method ; ε-subgradient ; nondifferentiable optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract A generalized subgradient method is considered which uses the subgradients at previous iterations as well as the subgradient at current point. This method is a direct generalization of the usual subgradient method. We provide two sets of convergence conditions of the generalized subgradient method. Our results provide a larger class of sequences which converge to a minimum point and more freedom of adjustment to accelerate the speed of convergence.
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    URL: http://dx.doi.org/10.1007/BF01594925
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  • 73
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    Digitale Medien
    On the convergence of the exponential multiplier method for convex programming (1993)
    Springer
    Mathematical programming 60 (1993), S. 1-19 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Convex programming ; linear programming ; multiplier method ; exponential penalty ; Augmented Lagrangian
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy “proximal” term in place of a quadratic. We strengthen substantially the available convergence results for these methods, and we derive the convergence rate of these methods when applied to linear programs.
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    URL: http://dx.doi.org/10.1007/BF01580598
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  • 74
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    Digitale Medien
    Lower subdifferentiability of quadratic functions (1993)
    Springer
    Mathematical programming 60 (1993), S. 93-113 
    Details
    ISSN: 1436-4646
    Schlagwort(e): 26B25 ; 90C20 ; Quadratic functions ; quasiconvexity ; subdifferentiability ; cutting plane methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper we characterize those quadratic functions whose restrictions to a convex set are boundedly lower subdifferentiable and, for the case of closed hyperbolic convex sets, those which are lower subdifferentiable but not boundedly lower subdifferentiable. Once characterized, we will study the applicability of the cutting plane algorithm of Plastria to problems where the objective function is quadratic and boundedly lower subdifferentiable.
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    URL: http://dx.doi.org/10.1007/BF01580603
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  • 75
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    Digitale Medien
    Polyhedral study of the capacitated vehicle routing problem (1993)
    Springer
    Mathematical programming 60 (1993), S. 21-52 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Vehicle routing ; polyhedron ; facet ; branch and cut
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The capacitated vehicle routing problem (CVRP) considered in this paper occurs when goods must be delivered from a central depot to clients with known demands, usingk vehicles of fixed capacity. Each client must be assigned to exactly one of the vehicles. The set of clients assigned to each vehicle must satisfy the capacity constraint. The goal is to minimize the total distance traveled. When the capacity of the vehicles is large enough, this problem reduces to the famous traveling salesman problem (TSP). A variant of the problem in which each client is visited by at least one vehicle, called the graphical vehicle routing problem (GVRP), is also considered in this paper and used as a relaxation of CVRP. Our approach for CVRP and GVRP is to extend the polyhedral results known for TSP. For example, the subtour elimination constraints can be generalized to facets of both CVRP and GVRP. Interesting classes of facets arise as a generalization of the comb inequalities, depending on whether the depot is in a handle, a tooth, both or neither. We report on the optimal solution of two problem instances by a cutting plane algorithm that only uses inequalities from the above classes.
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    URL: http://dx.doi.org/10.1007/BF01580599
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  • 76
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    Digitale Medien
    On the computation of weighted analytic centers and dual ellipsoids with the projective algorithm (1993)
    Springer
    Mathematical programming 60 (1993), S. 81-92 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Projective algorithm ; analytic centers ; dual ellipsoids
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The primal projective algorithm for linear programs with unknown optimal objective function value is extended to the case where one uses a weighted Karmarkar potential function. This potential is defined with respect to a strict lower bound to the optimum. The minimization of this potential when the lower bound is kept fixed, yields a primal and a dual feasible solution. The dual solution is the weighted analytic center of a certain dual polytope. Finally one exhibits a pair of homothetic dual ellipsoids that extends results obtained by Sonnevend, Todd, Ye, Freund and Anstreicher.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01580602
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  • 77
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    Survivable networks, linear programming relaxations and the parsimonious property (1993)
    Springer
    Mathematical programming 60 (1993), S. 145-166 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Network design ; LP relaxations ; worst-case analysis ; heuristics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We consider the survivable network design problem — the problem of designing, at minimum cost, a network with edge-connectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and thek-edge-connected network design problem. We establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the problem. The parsimonious property has numerous consequences. For example, we derive various structural properties of these LP relaxations, we present some algorithmic improvements and we perform tight worst-case analyses of two heuristics for the survivable network design problem.
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    URL: http://dx.doi.org/10.1007/BF01580607
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  • 78
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    Digitale Medien
    Updating of conjugate direction matrices using members of Broyden's family (1993)
    Springer
    Mathematical programming 60 (1993), S. 167-185 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Conjugate directions ; linear constraints ; matrix factorizations ; nonlinear optimization ; updating ; variable metric algorithms
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Many iterative algorithms for optimization calculations use a second derivative approximation,B say, in order to calculate the search directiond = −B −1∇f(x). In order to avoid invertingB we work with matricesZ, whose columns satisfy the conjugacy relationsZ T BZ = I. We present an update ofZ that is compatible with members of the Broyden family that generate positive definite second derivative approximations. The algorithm requires only 3n 2+O(n) flops for the update ofZ and the calculation ofd. The columns of the resultantZ matrices have interesting conjugacy and orthogonality properties with respect to previous second derivative approximations and function gradients, respectively. The update also provides a simple proof of Dixon's theorem. For the BFGS method we adapt the algorithm in order to obtain a null space method for linearly constrained calculations.
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    URL: http://dx.doi.org/10.1007/BF01580608
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  • 79
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    Digitale Medien
    Concave minimization via conical partitions and polyhedral outer approximation (1991)
    Springer
    Mathematical programming 50 (1991), S. 259-274 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Concave minimization ; global optimization ; nonlinear programming ; nonconvex programming ; branch-and-bound ; outer approximation ; cutting planes
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract An algorithm is proposed for globally minimizing a concave function over a compact convex set. This algorithm combines typical branch-and-bound elements like partitioning, bounding and deletion with suitably introduced cuts in such a way that the computationally most expensive subroutines of previous methods are avoided. In each step, essentially only few linear programming problems have to be solved. Some preliminary computational results are reported.
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    URL: http://dx.doi.org/10.1007/BF01594938
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  • 80
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    Digitale Medien
    Use of dynamic trees in a network simplex algorithm for the maximum flow problem (1991)
    Springer
    Mathematical programming 50 (1991), S. 277-290 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Algorithms ; complexity ; data structures ; dynamic trees ; graphs ; linear programming ; maximum flow ; network flow ; network optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Goldfarb and Hao (1990) have proposed a pivot rule for the primal network simplex algorithm that will solve a maximum flow problem on ann-vertex,m-arc network in at mostnm pivots and O(n 2 m) time. In this paper we describe how to extend the dynamic tree data structure of Sleator and Tarjan (1983, 1985) to reduce the running time of this algorithm to O(nm logn). This bound is less than a logarithmic factor larger than those of the fastest known algorithms for the problem. Our extension of dynamic trees is interesting in its own right and may well have additional applications.
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    URL: http://dx.doi.org/10.1007/BF01594940
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  • 81
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    The primal-dual algorithm as a constraint-set-manipulation device (1991)
    Springer
    Mathematical programming 50 (1991), S. 343-357 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Primal—dual algorithm ; continuity of value functional ; asymptotic feasibility ; constraint-set-manipulation ; entropy maximization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract A general primal—dual algorithm for linearly constrained optimization problems is formulated in which the dual variables are updated by a dual algorithmic operator. Convergence is proved under the assumption that the dual algorithmic operator implies asymptotic feasibility of the primal iterates with respect to the linear constraints. A general result relating the minimal values of an infinite sequence of constrained problems to the minimal value of a limiting problem (constrained by the limit of the sequence of constraints sets) is established and invoked. The applicability of the general theory is demonstrated by analyzing a specific dual algorithmic operator. This leads to the “MART” algorithm for constrained entropy maximization used in image reconstruction from projections.
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    URL: http://dx.doi.org/10.1007/BF01594943
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  • 82
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    An $$O(\sqrt n L)$$ iteration potential reduction algorithm for linear complementarity problems (1991)
    Springer
    Mathematical programming 50 (1991), S. 331-342 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Potential reduction algorithm ; linear complementarity problem ; interior point algorithm ; Karmarkar's algorithm ; path of centers ; central trajectory
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper proposes an interior point algorithm for a positive semi-definite linear complementarity problem: find an (x, y)∈ℝ 2n such thaty=Mx+q, (x,y)⩾0 andx T y=0. The algorithm reduces the potential function $$f(x,y) = (n + \sqrt n )\log x^T y - \sum\limits_{i = 1}^n {\log x_i y_i } $$ by at least 0.2 in each iteration requiring O(n 3) arithmetic operations. If it starts from an interior feasible solution with the potential function value bounded by $$O(\sqrt n L)$$ , it generates, in at most $$O(\sqrt n L)$$ iterations, an approximate solution with the potential function value $$ - O(\sqrt n L)$$ , from which we can compute an exact solution in O(n 3) arithmetic operations. The algorithm is closely related with the central path following algorithm recently given by the authors. We also suggest a unified model for both potential reduction and path following algorithms for positive semi-definite linear complementarity problems.
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    URL: http://dx.doi.org/10.1007/BF01594942
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  • 83
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    Finite termination of the proximal point algorithm (1991)
    Springer
    Mathematical programming 50 (1991), S. 359-366 
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    ISSN: 1436-4646
    Schlagwort(e): Sharp minima ; proximal point ; finite termination
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper concerns the notion of a sharp minimum on a set and its relationship to the proximal point algorithm. We give several equivalent definitions of the property and use the notion to prove finite termination of the proximal point algorithm.
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    URL: http://dx.doi.org/10.1007/BF01594944
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  • 84
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    Karmarkar's linear programming algorithm and Newton's method (1991)
    Springer
    Mathematical programming 50 (1991), S. 291-330 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Karmarkar's algorithm ; modified Newton's method ; global Newton's method ; projective transformation ; logarithmic barrier function ; nonlinear optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper describes a full-dimensional version of Karmarkar's linear programming algorithm, theprojective scaling algorithm, which is defined for any linear program in ℝ n having a bounded, full-dimensional polytope of feasible solutions. If such a linear program hasm inequality constraints, then it is equivalent under an injective affine mappingJ:ℝ n →ℝ m to Karmarkar's original algorithm for a linear program in ℝ m havingm—n equality constraints andm inequality constraints. Karmarkar's original algorithm minimizes a potential functiong(x), and the projective scaling algorithm is equivalent to that version of Karmarkar's algorithm whose step size minimizes the potential function in the step direction. The projective scaling algorithm is shown to be a global Newton method for minimizing a logarithmic barrier function in a suitable coordinate system. The new coordinate system is obtained from the original coordinate system by a fixed projective transformationy = Ф(x) which maps the hyperplaneH opt ={x:〈c, x〉 =c 0} specified by the optimal value of the objective function to the “hyperplane at infinity”. The feasible solution set is mapped underФ to anunbounded polytope. Letf LB(y) denote the logarithmic barrier function associated to them inequality constraints in the new coordinate system. It coincides up to an additive constant with Karmarkar's potential function in the new coordinate system. Theglobal Newton method iterate y * for a strictly convex functionf(y) defined on a suitable convex domain is that pointy * that minimizesf(y) on the search ray {y+λ v N(y): λ≧0} wherev N(y) =−(∇2 f(y))−1(∇f(y)) is the Newton's method vector. If {x (k)} are a set of projective scaling algorithm iterates in the original coordinate system andy (k) =Ф(x (k)) then {y (k)} are a set of global Newton method iterates forf LB(y) and conversely. Karmarkar's algorithm with step size chosen to minimize the potential function is known to converge at least at a linear rate. It is shown (by example) that this algorithm does not have a superlinear convergence rate.
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    URL: http://dx.doi.org/10.1007/BF01594941
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  • 85
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    Finding all maximal efficient faces in multiobjective linear programming (1993)
    Springer
    Mathematical programming 61 (1993), S. 357-375 
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    ISSN: 1436-4646
    Schlagwort(e): Multiobjective linear programming ; efficient set ; degeneracy ; simplex algorithm
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract An algorithm for finding the whole efficient set of a multiobjective linear program is proposed. From the set of efficient edges incident to a vertex, a characterization of maximal efficient faces containing the vertex is given. By means of the lexicographic selection rule of Dantzig, Orden and Wolfe, a connectedness property of the set of dual optimal bases associated to a degenerate vertex is proved. An application of this to the problem of enumerating all the efficient edges incident to a degenerate vertex is proposed. Our method is illustrated with numerical examples and comparisons with Armand—Malivert's algorithm show that this new algorithm uses less computer time.
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    URL: http://dx.doi.org/10.1007/BF01582157
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  • 86
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    Digitale Medien
    Series parallel composition of greedy linear programming problems (1993)
    Springer
    Mathematical programming 62 (1993), S. 1-14 
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    ISSN: 1436-4646
    Schlagwort(e): Greedy algorithm ; Monge arrays ; series parallel graphs ; linear programming ; network flow ; transportation problem ; integrality ; convexity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We study the concept of series and parallel composition of linear programming problems and show that greedy properties are inherited by such compositions. Our results are inspired by earlier work on compositions of flow problems. We make use of certain Monge properties as well as convexity properties which support the greedy method in other contexts.
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    URL: http://dx.doi.org/10.1007/BF01585157
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  • 87
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    Digitale Medien
    Min-cut clustering (1993)
    Springer
    Mathematical programming 62 (1993), S. 133-151 
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    ISSN: 1436-4646
    Schlagwort(e): Clustering ; decomposition ; column generation ; subproblem optimization ; valid inequality ; compiler design
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We describe a decomposition framework and a column generation scheme for solving a min-cut clustering problem. The subproblem to generate additional columns is itself an NP-hard mixed integer programming problem. We discuss strong valid inequalities for the subproblem and describe some efficient solution strategies. Computational results on compiler construction problems are reported.
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    URL: http://dx.doi.org/10.1007/BF01585164
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  • 88
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    Ky Fan's N-matrices and linear complementarity problems (1993)
    Springer
    Mathematical programming 61 (1993), S. 351-356 
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    ISSN: 1436-4646
    Schlagwort(e): Classes of matrices ; linear complementarity problem
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We consider the linear complementarity problem (LCP),w=Az + q, w⩾0,z⩾0,w T z=0, when all the off-diagonal entries ofA are nonpositive (the class of Z-matrices), all the proper principal minors ofA are positive and the determinant ofA is negative (the class of almost P-matrices). We shall call this the class of F-matrices. We show that ifA is a Z-matrix, thenA is an F-matrix if and only if LCP(q, A) has exactly two solutions for anyq⩾0,q≠0, and has at most two solutions for any otherq.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01582156
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  • 89
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    Digitale Medien
    Characterization of perturbed mathematical programs and interval analysis (1993)
    Springer
    Mathematical programming 61 (1993), S. 377-384 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Perturbed convex programs ; interval analysis ; sensitivity analysis ; nonlinear programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Several authors have used interval arithmetic to deal with parametric or sensitivity analysis in mathematical programming problems. Several reported computational experiments have shown how interval arithmetic can provide such results. However, there has not been a characterization of the resulting solution interval in terms of the usual sensitivity analysis results. This paper presents a characterization of perturbed convex programs and the resulting solution intervals. Interval arithmetic was developed as a mechanism for dealing with the inherent error associated with numerical computations using a computational device. Here it is used to describe error in the parameters. We show that, for convex programs, the resulting solution intervals can be characterized in terms of the usual sensitivity analysis results. It has been often reported in the literature that even well behaved convex problems can exhibit pathological behavior in the presence of data perturbations. This paper uses interval arithmetic to deal with such problems, and to characterize the behavior of the perturbed problem in the resulting interval. These results form the foundation for future computational studies using interval arithmetic to do nonlinear parametric analysis.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01582158
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  • 90
    Digitale Medien
    Digitale Medien
    A simple constraint qualification in convex programming (1993)
    Springer
    Mathematical programming 61 (1993), S. 385-397 
    Details
    ISSN: 1436-4646
    Schlagwort(e): 90C25 ; 90C29 ; Constraint qualification ; convex program ; optimality condition ; multi-objective program
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We introduce and characterize a class of differentiable convex functions for which the Karush—Kuhn—Tucker condition is necessary for optimality. If some constraints do not belong to this class, then the characterization of optimality generally assumes an asymptotic form. We also show that for the functions that belong to this class in multi-objective optimization, Pareto solutions coincide with strong Pareto solutions,. This extends a result, well known for the linear case.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01582159
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  • 91
    Digitale Medien
    Digitale Medien
    Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality (1993)
    Springer
    Mathematical programming 62 (1993), S. 69-83 
    Details
    ISSN: 1436-4646
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The problem of integer programming in bounded variables, over constraints with no more than two variables in each constraint is NP-complete, even when all variables are binary. This paper deals with integer linear minimization problems inn variables subject tom linear constraints with at most two variables per inequality, and with all variables bounded between 0 andU. For such systems, a 2-approximation algorithm is presented that runs in time O(mnU 2 log(Un 2 m)), so it is polynomial in the input size if the upper boundU is polynomially bounded. The algorithm works by finding first a super-optimal feasible solution that consists of integer multiples of 1/2. That solution gives a tight bound on the value of the minimum. It furthermore has an identifiable subset of integer components that retain their value in an integer optimal solution of the problem. These properties are a generalization of the properties of the vertex cover problem. The algorithm described is, in particular, a 2-approximation algorithm for the problem of minimizing the total weight of true variables, among all truth assignments to the 2-satisfiability problem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585160
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  • 92
    Digitale Medien
    Digitale Medien
    On the bigℳ in the affine scaling algorithm (1993)
    Springer
    Mathematical programming 62 (1993), S. 85-93 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Bigℳ ; affine scaling algorithm ; linear program ; interior point algorithm ; infeasibility ; global convergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract When we apply the affine scaling algorithm to a linear program, we usually construct an artificial linear program having an interior feasible solution from which the algorithm starts. The artificial linear program involves a positive number called the bigℳ. Theoretically, there exists anℳ * such that the original problem to be solved is equivalent to the artificial linear program ifℳ 〉ℳ *. Practically, however, such anℳ * is unknown and a safe estimate ofℳ is often too large. This paper proposes a method of updatingℳ to a suitable value during the iteration of the affine scaling algorithm. Asℳ becomes large, the method gives information on infeasibility of the original problem or its dual.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585161
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  • 93
    Digitale Medien
    Digitale Medien
    Staircase transportation problems with superadditive rewards and cumulative capacities (1993)
    Springer
    Mathematical programming 62 (1993), S. 199-213 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Transportation problem ; assignment problem ; supply ; demand ; staircase ; capacity ; lattice ; sublattice ; superadditive ; subadditive ; greatest element ; myopic ; greedy ; integral ; linear time ; complexity ; bivariate distribution ; correlation ; distribution ; substitution ; inventory ; age ; FIFO ; LIFO
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585166
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  • 94
    Digitale Medien
    Digitale Medien
    Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices (1993)
    Springer
    Mathematical programming 62 (1993), S. 321-357 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nonsmooth optimization ; convex composite optimization ; generalized gradient ; maximum eigenvalue ; sum of eigenvalues
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The sum of the largest eigenvalues of a symmetric matrix is a nonsmooth convex function of the matrix elements. Max characterizations for this sum are established, giving a concise characterization of the subdifferential in terms of a dual matrix. This leads to a very useful characterization of the generalized gradient of the following convex composite function: the sum of the largest eigenvalues of a smooth symmetric matrix-valued function of a set of real parameters. The dual matrix provides the information required to either verify first-order optimality conditions at a point or to generate a descent direction for the eigenvalue sum from that point, splitting a multiple eigenvalue if necessary. Connections with the classical literature on sums of eigenvalues and eigenvalue perturbation theory are discussed. Sums of the largest eigenvalues in the absolute value sense are also addressed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585173
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  • 95
    Digitale Medien
    Digitale Medien
    Nonsingularity and symmetry for linear normal maps (1993)
    Springer
    Mathematical programming 62 (1993), S. 415-425 
    Details
    ISSN: 1436-4646
    Schlagwort(e): 90C20 ; 90C30 ; 90C31 ; 90C33 ; Normal maps ; nonsingularity ; sensitivity analysis ; nonlinear programming ; quadratic programming ; complementarity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Normal maps are single-valued, generally nonsmooth functions expressing conditions for the solution of variational problems such as those of optimization or equilibrium. Normal maps arising from linear transformations are particularly important, both in their own right and as predictors of the behavior of related nonlinear normal maps. They are called (locally or globally)nonsingular if the functions appearing in them are (local or global) homeomorphisms satisfying a Lipschitz condition. We show here that when the linear transformation giving rise to such a normal map has a certain symmetry property, the necessary and sufficient condition for nonsingularity takes a particularly simple and convenient form, being simply a positive definiteness condition on a certain subspace.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585176
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  • 96
    Digitale Medien
    Digitale Medien
    The least element property of center location on tree networks with applications to distance and precedence constrained problems (1993)
    Springer
    Mathematical programming 62 (1993), S. 475-496 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Center location ; tree networks ; least element property
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In the classicalp-center location model on a network there is a set of customers, and the primary objective is to selectp service centers that will minimize the maximum distance of a customer to a closest center. Suppose that thep centers receive their supplies from an existing central depot on the network, e.g. a warehouse. Thus, a secondary objective is to locate the centers that optimize the primary objective “as close as possible” to the central depot. We consider tree networks and twop-center models. We show that the set of optimal solutions to the primary objective has a semilattice structure with respect to some natural ordering. Using this property we prove that there is ap-center solution to the primary objective that simultaneously minimizes every secondary objective function which is monotone nondecreasing in the distances of thep centers from the existing central depot. Restricting the location models to a rooted path network (real line) we prove that the above results hold for the respective classicalp-median problems as well.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585179
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  • 97
    Digitale Medien
    Digitale Medien
    Pivoting to normalize a basic matrix (1993)
    Springer
    Mathematical programming 62 (1993), S. 553-556 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Pivoting ; normalize ; basic matrix
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Given a matrix in basic form a sequence of pivots is described which brings the matrix into a basic form where the maximum absolute component is unity.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585183
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  • 98
    Digitale Medien
    Digitale Medien
    Using copositivity for global optimality criteria in concave quadratic programming problems (1993)
    Springer
    Mathematical programming 62 (1993), S. 575-580 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Non-convex non-linear programming ; global optimization ; second-order optimality conditions ; copositive matrices ; quadratic programming ; convex maximization problem
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this note we specify a necessary and sufficient condition for global optimality in concave quadratic minimization problems. Using this condition, it follows that, from the perspective of worst-case complexity of concave quadratic problems, the difference between local and global optimality conditions is not as large as in general. As an essential ingredient, we here use theε-subdifferential calculus via an approach of Hiriart-Urruty and Lemarechal (1990).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585185
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  • 99
    Digitale Medien
    Digitale Medien
    A Farkas lemma for difference sublinear systems and quasidifferentiable programming (1994)
    Springer
    Mathematical programming 63 (1994), S. 109-125 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Alternative theorems ; quasidifferentiable programming ; nonsmooth analysis ; optimality conditions ; difference convex programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract A new generalized Farkas theorem of the alternative is presented for systems involving functions which can be expressed as the difference of sublinear functions. Various other forms of theorems of the alternative are also given using quasidifferential calculus. Comprehensive optimality conditions are then developed for broad classes of infinite dimensional quasidifferentiable programming problems. Applications to difference convex programming and infinitely constrained concave minimization problems are also discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01582061
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  • 100
    Digitale Medien
    Digitale Medien
    A deep cut ellipsoid algorithm for convex programming: Theory and applications (1994)
    Springer
    Mathematical programming 63 (1994), S. 83-108 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Convex programming ; deep cut ellipsoid algorithm ; rate of convergence ; location theory ; min—max programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper proposes a deep cut version of the ellipsoid algorithm for solving a general class of continuous convex programming problems. In each step the algorithm does not require more computational effort to construct these deep cuts than its corresponding central cut version. Rules that prevent some of the numerical instabilities and theoretical drawbacks usually associated with the algorithm are also provided. Moreover, for a large class of convex programs a simple proof of its rate of convergence is given and the relation with previously known results is discussed. Finally some computational results of the deep and central cut version of the algorithm applied to a min—max stochastic queue location problem are reported.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01582060
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