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On a Method of Feasible Directions for Solving Variational Inequalities
Optimization, 1985An algorithm of the method of feasible directions is described solving effectively extremal problems which arise by the discretization of variational inequalities. Using the maximum principle the convergence of the algorithm is shown and some numerical examples are given.
H. Kirsten, R. Tichatschke
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The method of feasible directions for minimax problems
Optimization, 1992A general concept of converging algorithms of feasible direction type is introduced using upper approximation functions of the objective. By this means the zigzagging effect can be avoided and convergence to inf-stationary points of the objective is proved.
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SIAM Journal on Optimization, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amir Beck, Nadav Hallak
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amir Beck, Nadav Hallak
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Feasible direction method for bilevel programming problem
Optimization, 2012In this article, we investigate the application of feasible direction method for an optimistic non-linear bilevel programming problem. The convex lower level problem of an optimistic non-linear bilevel programming problem is replaced by relaxed KKT conditions. The feasible direction method developed by Topkis and Veinott [D.M.
Ayalew Getachew Mersha, Stephan Dempe
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Constrained Variable Metric Method With Feasible Directions
16th Design Automation Conference: Volume 2 — Optimal Design and Mechanical Systems Analysis, 1990Abstract This paper proposes a new feasible direction algorithm based on the constrained variable metric method of Powell in order to handle the design optimization problmes which demand that all iterative points are feasible. The algorithm retains many advantages of the constrained variable metric method, makes use of the properties of ...
Wang Jianhua, Zhou Ji, Yu Jun
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A stochastic approximation counterpart of the feasible direction method
Statistics & Probability Letters, 1987A stochastic approximation counterpart of the feasible direction method of Topkis and Veinott is considered. No convexity condition on a function to be minimized is imposed and a procedure for one-dimensional minimization along each feasible direction chosen is included.
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A feasible-direction method for nonlinear constrained optimization
ANNALI DELL UNIVERSITA DI FERRARA, 2002The author considers a feasible-direction interior-point technique for the solution of nonlinear differentiable constrained optimization problems which was originally introduced by Herskovits. In the paper several updating rules for the parameters used in the algorithm are introduced and corresponding convergence properties are shown.
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A new feasible directions method in nonlinear optimization
1992In each of the mechanical and discrete numerical models presented in the preceding chapters, the solution of a large nonlinear constrained optimization problem is required in order to evaluaute the actual residual stresses in body.
J. Orkisz, M. Pazdanowski
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Convergence of methods of feasible directions in extremal problems
USSR Computational Mathematics and Mathematical Physics, 1971Abstract GENERAL theorems on the convergence conditions of one-step iteration methods for minimization problems with constraints are presented. These theorems are applied for the uniform derivation of both previously known and also new results on the convergence of specific methods. The problem of the minimization of the functional f(x) on the set Q
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Generalized reduced gradient method as an extension of feasible direction methods
Journal of Optimization Theory and Applications, 1977The paper presents modifications of the generalized reduced gradient method which allows for a convergence proof. For that, a special construction of the basis is introduced, and some tools of the theory of feasible direction are used to modify the common choice of the direction at every step.
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