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 language | English |
|---|---|
| Pages (from-to) | 62-66 |
| Number of pages | 5 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | AC-25 |
| Issue number | 1 |
| Publication status | Published - 1980 Feb |
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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 journal › Article
}
TY - JOUR
T1 - NECESSARY CONDITIONS FOR MIN-MAX PROBLEMS AND ALGORITHMS BY A RELAXATION PROCEDURE.
AU - Shimizu, Kiyotaka
AU - Aiyoshi, Eitaro
PY - 1980/2
Y1 - 1980/2
N2 - 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.
AB - 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.
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UR - http://www.scopus.com/inward/citedby.url?scp=0018986069&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0018986069
VL - AC-25
SP - 62
EP - 66
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 1
ER -