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  • Articles  (77)
  • Other Sources
  • kriging  (40)
  • Nonlinear programming  (37)
  • 1985-1989  (44)
  • 1980-1984  (33)
  • Mathematics  (77)
  • 1
    Electronic Resource
    Electronic Resource
    NLPQL: A fortran subroutine solving constrained nonlinear programming problems (1986)
    Springer
    Annals of operations research 5 (1986), S. 485-500 
    Details
    ISSN: 1572-9338
    Keywords: Nonlinear programming ; sequential quadratic programming method ; numerical implementation ; test results
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract NLPQL is a FORTRAN implementation of a sequential quadratic programming method for solving nonlinearly constrained optimization problems with differentiable objective and constraint functions. At each iteration, the search direction is the solution of a quadratic programming subproblem. This paper discusses the organization of NLPQL, including the formulation of the subproblem and the information that must be provided by a user. A summary is given of the performance of different algorithmic options of NLPQL on a collection of test problems (115 hand-selected or application problems, 320 randomly generated problems). The performance of NLPQL is compared with that of some other available codes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02022087
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  • 2
    Electronic Resource
    Electronic Resource
    Integrating modeling, algorithm design, and computational implementation to solve a large-scale non-linear mixed integer programming problem (1986)
    Springer
    Annals of operations research 5 (1986), S. 395-411 
    Details
    ISSN: 1572-9338
    Keywords: Nonlinear programming ; decomposition ; branch and bound ; network ; transportation ; mixed integer programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model. The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large dollar savings.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02022082
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  • 3
    Electronic Resource
    Electronic Resource
    A successive quadratic programming algorithm with global and superlinear convergence properties (1986)
    Springer
    Mathematical programming 35 (1986), S. 253-264 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear programming ; successive quadratic programming ; Maratos effect ; exact penalty function ; superlinear convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper presents a successive quadratic programming algorithm for solving general nonlinear programming problems. In order to avoid the Maratos effect, direction-finding subproblems are derived by modifying the second-order approximations to both objective and constraint functions of the problem. We prove that the algorithm possesses global and superlinear convergence properties.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580879
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  • 4
    Electronic Resource
    Electronic Resource
    Nonlinear programming and nonsmooth optimization by successive linear programming (1989)
    Springer
    Mathematical programming 43 (1989), S. 235-256 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear programming ; nonsmooth optimization ; global convergence ; superlinear convergence ; trust region method ; Coleman-Conn method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Methods are considered for solving nonlinear programming problems using an exactl 1 penalty function. LP-like subproblems incorporating a trust region constraint are solved successively both to estimate the active set and to provide a foundation for proving global convergence. In one particular method, second order information is represented by approximating the reduced Hessian matrix, and Coleman-Conn steps are taken. A criterion for accepting these steps is given which enables the superlinear convergence properties of the Coleman-Conn method to be retained whilst preserving global convergence and avoiding the Maratos effect. The methods generalize to solve a wide range of composite nonsmooth optimization problems and the theory is presented in this general setting. A range of numerical experiments on small test problems is described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582292
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  • 5
    Electronic Resource
    Electronic Resource
    Computable bounds on parametric solutions of convex problems (1988)
    Springer
    Mathematical programming 40 (1988), S. 213-221 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear programming ; convex programming ; sensitivity and stability analysis ; parametric solutions ; optimal solution bounds
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We present a new method for computing bounds on parametric solutions of convex problems. The approach is based on a uniform quadratic underestimation of the objective function and a simple technique for the calculation of bounds on the optimal value function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01580732
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  • 6
    Electronic Resource
    Electronic Resource
    Homotopy techniques in linear programming (1986)
    Springer
    Algorithmica 1 (1986), S. 529-535 
    Details
    ISSN: 1432-0541
    Keywords: Homotopy ; Linear programming ; Interior point methods ; Nonlinear programming ; Karmarkar's method ; Quadratic regularization ; Path-following
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this note, we consider the solution of a linear program, using suitably adapted homotopy techniques of nonlinear programming and equation solving that move through the interior of the polytope of feasible solutions. The homotopy is defined by means of a quadratic regularizing term in an appropriate metric. We also briefly discuss algorithmic implications and connections with the affine variant of Karmarkar's method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01840461
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  • 7
    Electronic Resource
    Electronic Resource
    Convergence of a Tuy-type algorithm for concave minimization subject to linear inequality constraints (1981)
    Springer
    Applied mathematics & optimization 7 (1981), S. 1-9 
    Details
    ISSN: 1432-0606
    Keywords: Nonlinear programming ; nonconvex programming ; concave minimization ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A modification of Tuy's cone splitting algorithm for minimizing a concave function subject to linear inequality constraints is shown to be convergent by demonstrating that the limit of a sequence of constructed convex polytopes contains the feasible region. No geometric tolerance parameters are required.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01442106
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  • 8
    Electronic Resource
    Electronic Resource
    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
    Keywords: geostatistics ; kriging ; variogram analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01029419
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  • 9
    Electronic Resource
    Electronic Resource
    Lognormal kriging—the general case (1982)
    Springer
    Mathematical geology 14 (1982), S. 475-499 
    Details
    ISSN: 1573-8868
    Keywords: kriging ; lognormal estimation ; conservation of lognormality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A theoretical study of the general case of the estimation of regionalized variables with a lognormal distribution is presented. The results of this study are compared to those obtained assuming conservation of lognormality. The numerical significance of the different solutions is illustrated by several simple examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01077535
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  • 10
    Electronic Resource
    Electronic Resource
    Variogram models for regional groundwater geochemical data (1982)
    Springer
    Mathematical geology 14 (1982), S. 629-644 
    Details
    ISSN: 1573-8868
    Keywords: variogram ; kriging ; interpolation ; contouring ; inverse distance weighting ; geochemical gradient
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Four variogram models for regional groundwater geochemical data are presented. These models were developed from an empirical study of the sample variograms for more than 10 elements in groundwaters from two geologic regions in the Plainview quandrangle, Texas. A procedure is given for the estimation of the variogram in the isotropic and anisotropic case. The variograms were found useful for quantifying the differences in spatial variability for elements within a geologic unit and for elements in different geologic units. Additionally, the variogram analysis enables assessment of the assumption of statistical independence of regional samples which is commonly used in many statistical procedures. The estimated variograms are used in computation of kriged estimates for the Plainview quadrangle data. The results indicate that an inverse distance weighting model was superior for prediction than simple kriging with the particular variograms used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01033884
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