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  • 1
    Digitale Medien
    Digitale Medien
    A differential equation approach to nonlinear programming (1980)
    Springer
    Mathematical programming 18 (1980), S. 155-168 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Constrained Optimization ; Differential Equation ; Global Solution ; Nonlinear Programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract A new method is presented for finding a local optimum of the equality constrained nonlinear programming problem. A nonlinear autonomous system is introduced as the base of the theory instead of usual approaches. The relation between critical points and local optima of the original optimization problem is proved. Asymptotic stability of the critical points is also proved. A numerical algorithm which is capable of finding local optima systematically at the quadratic rate of convergence is developed from a detailed analysis of the nature of trajectories and critical points. Some numerical results are given to show the efficiency of the method.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588311
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  • 2
    Digitale Medien
    Digitale Medien
    On the computational utility of posynomial geometric programming solution methods (1982)
    Springer
    Mathematical programming 22 (1982), S. 163-201 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Geometric Programming ; Code Comparisons ; Numerical Testing ; Nonlinear Programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Ten codes or code variants were used to solve the five equivalent posynomial GP problem formulations. Four of these codes were general NLP codes; six were specialized GP codes. A total of forty-two test problems was solved with up to twenty randomly generated starting points per problem. The convex primal formulation is shown to be intrinsically easiest to solve. The general purpose GRG code called OPT appears to be the most efficient code for GP problem solution. The reputed superiority of the specialized GP codes GGP and GPKTC appears to be largely due to the fact that these codes solve the convex primal formulation. The dual approaches are only likely to be competitive for small degree of difficulty, tightly constrained problems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581036
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  • 3
    Digitale Medien
    Digitale Medien
    A globally convergent constrained quasi-Newton method with an augmented lagrangian type penalty function (1982)
    Springer
    Mathematical programming 23 (1982), S. 75-86 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Constrained Optimization ; Global Convergence ; Nonlinear Programming ; Penalty Function ; Quasi-Newton Method
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The recently proposed quasi-Newton method for constrained optimization has very attractive local convergence properties. To force global convergnce of the method, a descent method which uses Zangwill's penalty function and an exact line search has been proposed by Han. In this paper a new method which adopts a differentiable penalty function and an approximate line is presented. The proposed penalty function has the form of the augmented Lagrangian function. An algorithm for updating parameters which appear in the penalty function is described. Global convergence of the given method is proved.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01583780
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  • 4
    Digitale Medien
    Digitale Medien
    A smoothing-out technique for min—max optimization (1980)
    Springer
    Mathematical programming 19 (1980), S. 61-77 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Optimization ; Nonlinear Programming ; Unconstrained Optimization ; Nondifferentiable Optimization ; Min—Max Problems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper, we suggest approximations for smoothing out the kinks caused by the presence of “max” or “min” operators in many non-smooth optimization problems. We concentrate on the continuous-discrete min—max optimization problem. The new approximations replace the original problem in some neighborhoods of the kink points. These neighborhoods can be made arbitrarily small, thus leaving the original objective function unchanged at almost every point ofR n . Furthermore, the maximal possible difference between the optimal values of the approximate problem and the original one, is determined a priori by fixing the value of a single parameter. The approximations introduced preserve properties such as convexity and continuous differentiability provided that each function composing the original problem has the same properties. This enables the use of efficient gradient techniques in the solution process. Some numerical examples are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581628
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  • 5
    Digitale Medien
    Digitale Medien
    Accelerated convergence for the Powell/Hestenes multiplier method (1980)
    Springer
    Mathematical programming 18 (1980), S. 197-214 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear Programming ; Constrained Optimization ; Augmented Lagrangian Methods ; Multiplier Methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract It is known that augmented Lagrangian or multiplier methods for solving constrained optimization problems can be interpreted as techniques for maximizing an augmented dual functionD c(λ). For a constantc sufficiently large, by considering maximizing the augmented dual functionD c(λ) with respect toλ, it is shown that the Newton iteration forλ based on maximizingD c(λ) can be decomposed into taking a Powell/Hestenes iteration followed by a Newton-like correction. Superimposed on the original Powell/Hestenes method, a simple acceleration technique is devised to make use of information from the previous iteration. For problems with only one constraint, the acceleration technique is equivalent to replacing the second (Newton-like) part of the decomposition by a finite difference approximation. Numerical results are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588314
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  • 6
    Digitale Medien
    Digitale Medien
    On optimality conditions for structured families of nonlinear programming problems (1982)
    Springer
    Mathematical programming 22 (1982), S. 82-92 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Generic Programming ; Optimality Conditions ; Nonlinear Programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Optimality conditions for families of nonlinear programming problems inR n are studied from a generic point of view. The objective function and some of the constraints are assumed to depend on a parameter, while others are held fixed. Techniques of differential topology are used to show that under suitable conditions, certain strong second-order conditions are necessary for optimality except possibly for parameter values lying in a negligible set.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581027
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  • 7
    Digitale Medien
    Digitale Medien
    Comparative computer results of a new complementary pivot algorithm for solving equality and inequality constrained optimization problems (1980)
    Springer
    Mathematical programming 18 (1980), S. 169-185 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear Programming ; Equality Constraints ; Fixed Points ; Complementary Pivoting Algorithms
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper reports the development of a new algorithm for solving the general constrained optimization problem (that of optimizing an objective function subject to both equality and inequality constraints). The approach is based on the complementary pivoting algorithms which have been developed to solve certain classes of fixed point problems. The specific approach is to use the equality constraints to solve for some variables in terms of the remaining ones thus enabling one to eliminate the equality constraints altogether. The result, under certain circumstances, is an optimization problem which may be transformed into a fixed point problem in such a way that a complementary pivoting code may be used to search for a solution. Seventeen test problems have been solved by this method and the results are compared against those obtained from GRG (Generalized Reduced Gradient method). The results of the tests indicate that the fixed point approach is robust (all 17 problems were solved by this method where as GRG solved 16). As to the computer times, the fixed point code proved to be as fast or faster than GRG on the lower dimensional problems; however, as the dimension increased, the trend reversed and on a 40 dimensional problem GRG was approximately 11 times faster. The conclusion from these tests is that when the dimension of the original problem can be reduced sufficiently by the equality constraints, the fixed point approach appears to be more effective than GRG.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588312
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  • 8
    Digitale Medien
    Digitale Medien
    Nonlinear programming via an exact penalty function: Global analysis (1982)
    Springer
    Mathematical programming 24 (1982), S. 137-161 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear Programming ; Exact Penalty Methods ; Successive Quadratic Programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper we motivate and describe an algorithm to solve the nonlinear programming problem. The method is based on an exact penalty function and possesses both global and superlinear convergence properties. We establish the global qualities here (the superlinear nature is proven in [7]). The numerical implementation techniques are briefly discussed and preliminary numerical results are given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585101
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  • 9
    Digitale Medien
    Digitale Medien
    Second-order conditions for an exact penalty function (1980)
    Springer
    Mathematical programming 19 (1980), S. 178-185 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear Programming ; Exact Penalty Function ; Constrained Optimization ; Piecewise Differentiable
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper we give first- and second-order conditions to characterize a local minimizer of an exact penalty function. The form of this characterization gives support to the claim that the exact penalty function and the nonlinear programming problem are closely related. In addition, we demonstrate that there exist arguments for the penalty function from which there are no descent directions even though these points are not minimizers.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581639
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  • 10
    Digitale Medien
    Digitale Medien
    A polynomially bounded algorithm for a singly constrained quadratic program (1980)
    Springer
    Mathematical programming 18 (1980), S. 338-343 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear Programming ; Convex Programming ; Quadratic Programming ; Singly Constrained Quadratic Program
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper presents a characterization of the solutions of a singly constrained quadratic program. This characterization is then used in the development of a polynomially bounded algorithm for this class of problems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01588328
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  • 11
    Digitale Medien
    Digitale Medien
    Nonlinear programming via an exact penalty function: Asymptotic analysis (1982)
    Springer
    Mathematical programming 24 (1982), S. 123-136 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear Programming ; Exact Penalty Methods ; Successive Quadratic Programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper we consider the final stage of a ‘global’ method to solve the nonlinear programming problem. We prove 2-step superlinear convergence. In the process of analyzing this asymptotic behavior, we compare our method (theoretically) to the popular successive quadratic programming approach.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585100
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  • 12
    Digitale Medien
    Digitale Medien
    The lognormal approach to predicting local distributions of selective mining unit grades (1980)
    Springer
    Mathematical geology 12 (1980), S. 285-303 
    Details
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; lognormal distribution ; mine planning ; ore reserve estimation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract When planning highly selective mining operations, the challenge is to estimate mineable ore reserves that will be selected at the mining stage. From exploration data it is not possible to estimate accurately the grade (or thickness) of each future selective mining unit; however, it is possible to estimate the local distributions of these mining unit grades within large panels suitable for long-range mine planning. Application of a cut-off then allows estimation of the recovered ore tonnage and grade within each such panel. Derivation of local conditional distributions is rather simple when the grade is either normally or lognormally distributed. The geologically important lognormal case is fully described both in the stationary and the nonstationary case. Cross validations of these techniques using the exploration data of the Imouraren uranium deposit are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01029417
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  • 13
    Digitale Medien
    Digitale Medien
    The random coin method: Solution of the problem of the simulation of a random function in the plane (1980)
    Springer
    Mathematical geology 12 (1980), S. 25-32 
    Details
    ISSN: 1573-8868
    Schlagwort(e): random function ; geostatistics ; simulation ; covariance
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract This paper presents a new geostatistical method to obtain realizations of stationary random functions in the plane.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01039901
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  • 14
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    Digitale Medien
    Disjunctive kriging: Comparison of theory with actual results (1980)
    Springer
    Mathematical geology 12 (1980), S. 305-320 
    Details
    ISSN: 1573-8868
    Schlagwort(e): disjunctive kriging ; logarithmic kriging ; gold evaluation ; geostatistics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The method of disjunctive kriging is applied to the evaluation of blocks of ore in a gold mine, and the estimated block values are compared with the true block values. First the theory of disjunctive kriging as applicable to mine valuation is presented from the user's viewpoint. The theory is then applied to process sample values originating from a large gold mine. Using the computer simulation of a number of sampling programs, estimated values and true values are compared. The disjunctive kriging estimates are also compared with estimates obtained by other methods of evaluation, including logarithmic kriging. It is shown that the results obtained, using real world data, are in complete agreement with the results expected according to the geostatistical theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01029418
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  • 15
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    Digitale Medien
    Statistical and geostatistical methods applied to the exploration work of the Nanisivik Zn-Pb mine, Baffin Island, Canada (1980)
    Springer
    Mathematical geology 12 (1980), S. 321-337 
    Details
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; kriging ; variogram analysis
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The Nanisivik Pb-Zn deposit at Strathcona Sound, northern Baffin Island, Canada, is an orebody that is an S-shaped lens 3000 m long, 75 m wide, and 2–20 m thick. It is an epigenetic karst channel filling. Total reserves are 6.9 million short tons of 14.12% Zn, 1.4% Pb, and 1.77 oz of Ag per ton. The mine was brought into production in 1976 at a rate of 2000 short tons per day. In the preproduction phase variogram studies based only on surface holes indicated a random distribution. For the evaluation of grades and for the determination of the confidence limits, classic statistical procedures were applied. Since the drilling density was different in different ore zones, a model was developed to test the effect of different drill hole spacings on the uncertainties in the present value in a discounted cash flow model. After the initial development and mining stage, structures could be recognized in semivariograms. Studies for a best drilling grid showed that the pattern of 25 ×20 m used in the mine could be extended to 35 ×35 m, taking into account that eight stopes are mined simultaneously. For ore reserve calculations weighing factors were calculated by kriging for six universally applicable geometric situations. Only the drill holes within a block and immediately surrounding it were taken into account. A test in a well-known zone yielded satisfactory results. A test to predict highs and lows of the grade accurately enough to optimally place the pillars failed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01029419
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  • 16
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    Digitale Medien
    The effect of drift on the experimental semivariogram (1982)
    Springer
    Mathematical geology 14 (1982), S. 309-319 
    Details
    ISSN: 1573-8868
    Schlagwort(e): Bias ; drift ; semivariogram ; geostatistics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract When nonlinear drift is present, the nature of the bias in the experimental semivariogram estimator of the semivariogram function is determined by the extent and density of the sampling as well as by the drift function itself. The bias caused by drift may affect the interpretation of the experimental semivariogram over its entire range.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01032592
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  • 17
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    Digitale Medien
    Prediction of local ore recoveries and ore-waste ratios at the silver bell uranium mine (1982)
    Springer
    Mathematical geology 14 (1982), S. 645-660 
    Details
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; uranium ; production forecast
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Geostatistical estimation techniques were customized to allow forecasting of production figures at the Silver Bell uranium mine (Uravan District).Surface drill hole data were used to provide a block model of kriged estimators of average uranium grades. Figures for recoverable ore grade and the ore-waste ratio are then deduced from regressive curves previously obtained from underground information and production data. Cross-validations of the entire model were performed and were found positive.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01033885
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  • 18
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    Digitale Medien
    The combination of sampling and kriging in the regional estimation of coal resources (1982)
    Springer
    Mathematical geology 14 (1982), S. 87-106 
    Details
    ISSN: 1573-8868
    Schlagwort(e): coal ; geostatistics ; kriging ; regional estimation ; systematic sampling
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Two-dimensional systematic sampling of small plots followed by the kriging of those plots may be employed to obtain regional estimates of coal resources and measures of the accuracy of the estimates. The use of sampling makes large savings in computation possible. Two case studies involving the estimation of coal tonnage are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01083946
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  • 19
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    Digitale Medien
    Exact formulas for approximating variogram function integrals (1980)
    Springer
    Mathematical geology 12 (1980), S. 577-588 
    Details
    ISSN: 1573-8868
    Schlagwort(e): variogram ; geostatistics ; estimation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a polygonal function the integral may be easily approximated by closed form representations of polygonal integrals. This approach provides a basis for more extensive statistical evaluation not evident in existing approximation methods. This paper provides the closed form representations for two-dimensional variogram functions whose domain is represented by a finite collection of rectangles.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01034745
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  • 20
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    Digitale Medien
    On the estimation of the generalized covariance function (1982)
    Springer
    Mathematical geology 14 (1982), S. 57-64 
    Details
    ISSN: 1573-8868
    Schlagwort(e): estimation ; generalized covariance function ; generalized increments ; geostatistics ; intrinsic random functions ; multicollinearity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The estimation of the generalized covariance function, K, is a major problem in the use of intrinsic random functions of order k to obtain kriging estimates. The precise estimation by least-squares regression of the parameters in polynomial models for K is made difficult by the nature of the distribution of the dependent variable and the multicollinearity of the independent variables.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01037447
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  • 21
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    Studies of the effects of outliers and data transformation on variogram estimates for a base metal and a gold ore body (1982)
    Springer
    Mathematical geology 14 (1982), S. 557-564 
    Details
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; variogram ; outliers
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Variograms for gold and lead values from the Loraine and Prieska mines, respectively, indicate that data outliers can seriously distort and/or mask the real variogram patterns. Studies show that this problem is best overcome for these mines by logarithmic transformation of the data, and/or a suitable screening out of such outliers, and/or more robust variogram estimation procedures; the benefits are particularly significant when the basic data is limited.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01033879
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  • 22
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    Digitale Medien
    Anisotropic hole-effect modeling (1982)
    Springer
    Mathematical geology 14 (1982), S. 217-239 
    Details
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; variograms ; anisotropies ; tungsten
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The regionalization of tungsten grades at the χ deposit represents an ideal case for anisotropic hole-effect variogram modeling. The modeling technique is presented step by step and the consequences of the model on block kriging are indicated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01032885
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  • 23
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    Digitale Medien
    Sequential sampling to contour an uncertain function (1982)
    Springer
    Mathematical geology 14 (1982), S. 387-404 
    Details
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; resource estimation ; geoexploration ; sampling
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Sampling exploration of uncertain functions to locate critical contour levels is most effective if sampling decisions are made sequentially. A simple sequential exploration strategy, based on pseudo-Bayesian second-moment analysis, is proposed and compared with non-sequential systematic sampling. Repeated application to functions simulated pseudorandomly from stationary random processes on the line and on the plane indicates uniform superiority of the sequential strategy. The method is particularly advantageous when the function of interest,h(X), has an uncertain trend, and in general when the random process that quantifies prior uncertainty onh(X) is highly correlated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01077529
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  • 24
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    Digitale Medien
    Geostatistical case studies of the advantages of lognormal-de Wijsian kriging with mean for a base metal mine and a gold mine (1982)
    Springer
    Mathematical geology 14 (1982), S. 547-555 
    Details
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; kriging
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Parallel variogram analyses, block kriging, and follow-up studies were effected for the lead content of part of the Prieska copper-zinc ore body and for the gold content of the highly variable Breef in a section of the Loraine gold mine, based first on untransformed values and second on logarithmically transformed values using the lognormal-de Wijsian model. For both models the effect was also analyzed of using the population mean or ignoring it. Practical follow-up comparisons confirm theoretical considerations and show that on these mines conditional biases can be eliminated conveniently by kriging with mean; also that the lognormal-de Wijsian model with mean gives the best results.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01033878
    Standort Signatur Erwartet Verfügbarkeit
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