A Frank-Wolfe Type Theorem for Convex Polynomial Programs

In 1956, Frank and Wolfe extended the fundamental existence theorem of linear programming by proving that an arbitrary quadratic function f attains its minimum over a nonempty convex polyhedral set X provided f is bounded from below over X. We show that a similar statement holds if f is a convex pol...

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Veröffentlicht in:Computational optimization and applications 2002-04, Vol.22 (1), p.37-48
Hauptverfasser: Belousov, Evgeny G, Klatte, Diethard
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description In 1956, Frank and Wolfe extended the fundamental existence theorem of linear programming by proving that an arbitrary quadratic function f attains its minimum over a nonempty convex polyhedral set X provided f is bounded from below over X. We show that a similar statement holds if f is a convex polynomial and X is the solution set of a system of convex polynomial inequalities. In fact, this result was published by the first author already in a 1977 book, but seems to have been unnoticed until now. Further, we discuss the behavior of convex polynomial sets under linear transformations and derive some consequences of the Frank-Wolfe type theorem for perturbed problems. [PUBLICATION ABSTRACT]
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subjects Linear programming
Mathematical programming
Optimization
Polynomials
Recessions
Studies
title A Frank-Wolfe Type Theorem for Convex Polynomial Programs
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