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Methods of Feasible Directions: A Review

2000
Since the theoretical basis for the method of feasible directions (MFD) was originally developed by Zoutendijk in 1960’s, several basic variations and modifications of MFD were proposed and investigated. Even though faster algorithms for solving nonlinear programming problems exist, MFD has never been abandoned because of several important advantages ...
Xibin Chen, Michael M. Kostreva
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A new SQP method of feasible directions for nonlinear programming

Applied Mathematics and Computation, 2004
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhibin Zhu, Kecun Zhang
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Self-Tuning Norm-Relaxed Method of Feasible Directions

Journal of Optimization Theory and Applications, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Korycki, J., Kostreva, M.
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Enhanced methods of feasible directions for engineering design problems

Journal of Optimization Theory and Applications, 1986
After the advantages of methods of feasible directions in an engineering design environment are pointed out, several modifications to the classical scheme are proposed, aimed at improving computational efficiency while preserving convergence properties.
Tits, A. L.   +2 more
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Feasible direction methods in the absence of slater's condition

Mathematische Operationsforschung und Statistik. Series Optimization, 1978
Three popular feasible direction methods for solving convex programming problems are reformulated so that they now work in the absence of Slater’s condition or any other constraint qualification.
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Combined phase I—phase II methods of feasible directions

Mathematical Programming, 1979
This paper presents several new algorithms, generalizing feasible directions algorithms, for the nonlinear programming problem, min{f 0 (z) ∣f j (z) ≤ 0,j = 1, 2, ⋯ ,m}. These new algorithms do not require an initial feasible point.
Elijah Polak   +2 more
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An optimization algorithm based on the method of feasible directions

Structural Optimization, 1995
The theory and implementation of an optimization algorithm code based on the method of feasible directions are presented. Although the method of feasible directions was developed during the 1960's, the present implementation of the algorithm includes several modifications to improve its robustness.
A. D. Belegundu, L. Berke, S. N. Patnaik
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On a Method of Feasible Directions for Solving Variational Inequalities

Optimization, 1985
An 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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Parallel Line Search in Method of Feasible Directions

Optimization and Engineering, 2004
In this paper the line search procedure within the method of feasible directions is parallelized and used in the solution of constrained structural optimization problems. As the objective function is linear in the variables, the step size problem reduces to a zero finding problem. That is, the step size is the distance along the direction vector to the
Ashok D. Belegundu   +4 more
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The method of feasible directions for minimax problems

Optimization, 1992
A 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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