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GENERAL PARAMETRIC LINEAR FRACTIONAL programming

METRIKA 1972年第1期19卷 11-17页

作者： VARMA, GK MINIST DEF DIRECTORATE SCI EVALUATIONNEW DELHIINDIA

This paper deals with the behaviour of solutions to a linear fractional programming problem when the coefficients of the objective function are allowed to vary.

关键词： Objective Function Stochastic Process Probability Theory Economic Theory programming problem

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Generalized dynamic programming methods in integer programming

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Mathematical programming 1973年第1期4卷 222-232页

作者： Wolsey, Laurence A. Center For Operations Research and Econometrics Leuven Belgium

When regarded as a shortest route problem, an integer program can be seen to have a particularly simple structure. This allows the development of an algorithm for finding the kth best solution to an integer programmin... 详细信息

When regarded as a shortest route problem, an integer program can be seen to have a particularly simple structure. This allows the development of an algorithm for finding the k^th best solution to an integer programming problem with max{O(kmn), O(k log k)} operations. Apart from its value in the parametric study of an optimal solution, the approach leads to a general integer programming algorithm consisting of (1) problem relaxation, (2) solution of the relaxed problem parametrically by dynamic programming, and (3) generation of k^th best solutions until a feasible solution is found. Elementary methods based on duality for reducing k for a given problem relaxation are then outlined, and some examples and computational aspects are discussed. © 1973 The Mathematical programming Society.

关键词： Feasible Solution Mathematical Method Dynamic programming programming problem Parametric Study

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Minimum theorems for displacement and plastic strain rate histories in structural elastoplasticity

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Meccanica 1975年第2期10卷 99-106页

作者： Polizzotto, Castrenze Istituto di Scienza e Tecnica delle Costruzioni Facoltà di Architettura Università di Palermo Italy

The finite element method approach is used to obtain formulations of analysis problems relative to elastic-plastic structures when subjected to prescribed programmes of loads, and under the restrictive hypotheses:a) the yielding surfaces are piecewise linearized, and b) the plastic flow-laws are supposed to be of holonomic type within a single "finite" time interval. For mulations are given as linear complementarity problems and quadratic programming problems: one pair of formulations in terms of velocity and plastic multiplier rate histories, and another pair in terms of plastic multiplier rate histories only. The solutions are shown to be characterized by two minimum principles for displacement and plastic strain rate histories. After some general remarks about computational procedures, the paper is concluded with some suggestions for future developments. © 1975 Tamburini Editore s.p.a. Milano.

关键词： Finite Element Method programming problem Tempo Quadratic programming Yielding Surface

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Methods of solution of nonlinear extremal problems

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Cybernetics 1966年第4期2卷 1-14页

作者： Ermol'ev Yu.M. Institute of Cybernetics AS UkrSSR

In the present paper only general methods of solving mathematical programming problems have been considered, and special methods intended for solving problems of a definite class have not been touched upon. In particular, the method of dynamic programming has not been considered. The development of simple special methods is of paramount practical value. As a rule, a concrete extremal problem has essential peculiarities, because of which it is possible to conduct a more meaningful investigation than is possible in the general case, and thus obtain a simplified method of solution. © 1968 The Faraday Press, Inc.

关键词： Operating System Artificial Intelligence System Theory Dynamic programming programming problem

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Implicit function theorems for mathematical programming and for systems of inequalities

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Mathematical programming 1974年第1期6卷 141-156页

作者： Bigelow, James H. Shapiro, Norman Z. RAND Corporation Santa Monica California United States

Implicit function formulas for differentiating the solutions of mathematical programming problems satisfying the conditions of the Kuhn—Tucker theorem are motivated and rigorously demonstrated. The special case of a convex objective function with linear constraints is also treated with emphasis on computational details. An example, an application to chemical equililibrium problems, is given. Implicit function formulas for differentiating the unique solution of a system of simultaneous inequalities are also derived. © 1974, The Mathematical programming Society. All rights reserved.

关键词： Objective Function Unique Solution Mathematical Method programming problem Mathematical programming

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The generalized inverse in parametric programming

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Calcolo 1974年第3期11卷 351-363页

作者： Salinetti, G. Istituto di Calcolo delle Probabilità dell'Università di Roma Roma Italy

In this paper we are concerned with parametric programming problems. The main results are two: the first one is an explicit representation of the general optimal solution of particular parametric programming problems;the second one is an unified approach to general parametric programming problems. The method suggested here is based on the utilization of the generalized inverse of a matrix: it allows a fast and simple solution of parametric problems and has several advantages over the classical parametric methods. We refer to interval linear programming problems but a fruitful direction of research may be its application to linear programming problems in the standard from. © 1975 IAC.

关键词： programming problem Linear programming problem Null Space Generalize Inverse Parametric problem

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Convergence rate of a penalty-function scheme

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Journal of Optimization Theory and Applications 1971年第1期7卷 39-51页

作者： Luenberger, David G. Department of Engineering-Economic Systems Stanford University Stanford California United States

The penalty-function approach is an attractive method for solving constrained nonlinear programming problems, since it brings into play all of the well-developed unconstrained optimization techniques, If, however, the classical steepest-descent method is applied to the standard penalty-function objective, the rate of convergence approaches zero as the penalty coefficient is increased to yield a close approximation to the true solution. In this paper, it is shown that, if m+1 steps of the conjugate-gradient method are successively repeated (where m is the number of constraints), the convergence rate when applied to the penalty-function objective conveges at a rate predicted by the second derivative of the Lagrangian. This rate is independent of the penalty coefficient and, hence, the scheme yields reasonable convergence for a first-order method. © 1971 Plenum Publishing Corporation.

关键词： Convergence Rate programming problem Optimization Technique Nonlinear programming Close Approximation

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Rank restrictions on the quadratic form in indefinite quadratic programming

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Unternehmensforschung Operations Research - Recherche Opérationnelle 1971年第1期15卷 214-216页

作者： Amato, H. Mensch, G. Graduate School of Business Administration Tulane University New Orleans United States International Institute of Management Wissenschaftszentrum Berlin Germany

A quadratic programming problem, where q(x) =aTx +xTQx is an indefinite objective function, can be solved with Swarup's approach of optimizing (cTx + α)(dTx + β) only if the rank of Q is two;if Q is definite, th... 详细信息

A quadratic programming problem, where q(x) =a^Tx +x^TQx is an indefinite objective function, can be solved with Swarup's approach of optimizing (c^Tx + α)(d^Tx + β) only if the rank of Q is two;if Q is definite, the rank of Q must be one. © 1971 Physica-Verlag.

关键词： Objective Function Quadratic Form programming problem Quadratic programming Quadratic programming problem

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Duality for non-linear programming in a Banach space

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Unternehmensforschung Operations Research - Recherche Opérationnelle 1969年第4期13卷 291-295页

作者： Chandra, S. Department of Mathematics I.I.T. Kanpur India

A constrained maximization problem in a real Banach space is considered, where the objective function is a non-linear pseudo concave functional and constraints are given by m non linear quasi convex functionals. The optimality conditions and converse duality theorem, given by Ritter, have been extended to this class of programming problems. © 1969 Physica-Verlag.

关键词： Objective Function Optimality Condition programming problem Maximization problem Duality Theorem

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Economics of Planning 1978年第3期14卷 167-170页

作者： Sandblom, Carl-Louis Department of Quantitative Methods Concordia University Montreal H4B IR6 Quebec Lloyola Campus 7141 Sherbrooke Street West Canada

Decomposition methods can provide the rescue from the "curse of dimensionality", which often prevents the successful numerical solution of large scale nonlinear mathematical programming problems. A symmetric nonlinear decomposition theory has been elaborated by T.O.M. Kronsjö (4) as an extension of a theory by the same author (3). The stringent proof of the convergence of this decomposition algorithm requires some results on necessary optimality conditions for certain mathematical programming problems. In this paper we state and prove some theorems providing these results. © 1978 The Centre for Russian and East European Studies.

关键词： Economic Growth Optimality Condition programming problem Mathematical programming Economic System

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