NECESSARY CONDITIONS FOR MIN-MAX PROBLEMS AND ALGORITHMS BY A RELAXATION PROCEDURE.

Kiyotaka Shimizu, Eitaro Aiyoshi

Research output: Contribution to journalArticle

78 Citations (Scopus)

Abstract

For decision making under uncertainty, a rational optimality criterion is min-max. Min-max problems such that the minimizer makes an optimal decision against the worst case that might be chosen by the maximizer are studied. This study presents necessary conditions and computational methods for a min-mix solution (not a saddle point solution). Those conditions are stated in a form like Kuhn-Tucker theorem. The computational methods are based on the relaxation procedure. A min-max problem such that the minimizer and the maximizer are subject to separate constraints is primarily studied. But it is shown that the obtained results can be applied for the unseparate constraint case by use of duality theory.

Original languageEnglish
Pages (from-to)62-66
Number of pages5
JournalIEEE Transactions on Automatic Control
VolumeAC-25
Issue number1
Publication statusPublished - 1980 Feb

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Computational methods
Decision making
Uncertainty

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Cite this

NECESSARY CONDITIONS FOR MIN-MAX PROBLEMS AND ALGORITHMS BY A RELAXATION PROCEDURE. / Shimizu, Kiyotaka; Aiyoshi, Eitaro.

In: IEEE Transactions on Automatic Control, Vol. AC-25, No. 1, 02.1980, p. 62-66.

Research output: Contribution to journalArticle

Shimizu, Kiyotaka ; Aiyoshi, Eitaro. / NECESSARY CONDITIONS FOR MIN-MAX PROBLEMS AND ALGORITHMS BY A RELAXATION PROCEDURE. In: IEEE Transactions on Automatic Control. 1980 ; Vol. AC-25, No. 1. pp. 62-66.
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