Farkas' theorem of nonconvex type and its application to a min-max problem
type: Item
instance of: scholarly article
title: Farkas' theorem of nonconvex type and its application to a min-max problem
zbMATH Open document ID: 0621.49015
DOI: 10.1007/BF00938544
author: Y. Ishizuka
published in: Journal of Optimization Theory and Applications
publication date: 1988-01-01T00:00:00Z
review text: This note is concerned with the generalization of Farkas' theorem and its application to derive optimality conditions for a min-max problem. Farkas' theorem is generalized to a system of inequalities described by sup-min type positively homogeneous functions. This generalization allows us to deal with optimization problems consisting of objective and constraint functions whose directional derivatives are not necessarily convex with respect to the directions. As an example of such problems, we formulate a min-max problem and derive its optimality conditions.
Mathematics Subject Classification ID: 49K35
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 4007090
zbMATH Keywords: generalization of Farkas' theorem
zbMATH Keywords: optimality conditions
zbMATH Keywords: min-max problem
zbMATH Keywords: directional derivatives
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4007090