Generalized Farkas' theorem and optimization of infinitely constrained problems

K. Shimizu, E. Aiyoshi, R. Katayama

研究成果: Article査読

10 被引用数 (Scopus)

抄録

This note is concerned with the generalization of Farkas' theorem of the alternative and its application to derive the necessary optimality conditions for min-max problems with satisfaction conditions. Farkas' theorem is generalized to a system of linear inequalities with max operations. The problems studied require a solution at which the worst objective value attains its minimum over a set of solutions fulfilling satisfaction conditions. The satisfaction conditions claim that plural performance criteria should be kept below the permissible level, whatever disturbances may happen or whatever opponents' decisions may be taken. We present a generalized Farkas' theorem in order to derive the necessary optimality conditions for the problems of this class.

本文言語English
ページ(範囲)451-462
ページ数12
ジャーナルJournal of Optimization Theory and Applications
40
3
DOI
出版ステータスPublished - 1983 7 1

ASJC Scopus subject areas

  • 制御と最適化
  • 経営科学およびオペレーションズ リサーチ
  • 応用数学

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