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Convergence analysis of norm-relaxed method of feasible directions
Journal of Optimization Theory and Applications, 1996The paper studies the asymptotic rate of convergence of the norm-relaxed method of feasible directions in the case of solving the problem of minimizing a strictly convex function subject to convex inequality constraints, all the problems' functions being of class \(C^2\).
Korycki, J., Kostreva, M.
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Parallel Line Search in Method of Feasible Directions
Optimization and Engineering, 2004In 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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A Drivable Method of Feasible Directions
SIAM Journal on Control, 1973This paper presents a feasible directions algorithm for solving a general nonlinear programming problem. The algorithm is characterized by the fact that it is parametrized by functions. One may, through proper choice of the parametrizing maps, model the algorithm to optimize its behavior with respect to classes of problems.
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Rate of Convergence of a Class of Methods of Feasible Directions
SIAM Journal on Numerical Analysis, 1973This paper deals with the rate of convergence of four methods of feasible directions the Zoutendijk procedures 1 and 2 and two modifications of these procedures due to the authors. It is shown that of these methods, the two due to the authors converge linearly under convexity assumptions, that the Zoutendijk procedure 2 converges sublinearly under ...
Pironneau, O., Polak, E.
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Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method
INFORMS Journal on Computing, 2021Bilevel problems are highly challenging optimization problems that appear in many applications of energy market design, critical infrastructure defense, transportation, pricing, and so on. Often these bilevel models are equipped with integer decisions, which makes the problems even harder to solve.
Thomas Kleinert, Martin Schmidt
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A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions
Applied Mathematics and Optimization, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jian, Jin-bao +3 more
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Methods of Feasible Directions: A Review
2000Since 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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Feasible direction methods in the absence of slater's condition
Mathematische Operationsforschung und Statistik. Series Optimization, 1978Three 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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A comparison of feasible direction methods for the stochastic transportation problem
Computational Optimization and Applications, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daneva, Maria +3 more
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A Steepest Feasible Direction Extension of the Simplex Method
2020We present a feasible direction approach to general linear programming, which can be embedded in the simplex method although it works with non-edge feasible directions. The feasible direction used is the steepest in the space of all variables, or an approximation thereof.
Biressaw C. Wolde, Torbjörn Larsson
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