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Zbl 0631.90077
Ferro, F.
A minimax theorem for vector-valued functions. (English)
[J] J. Optimization Theory Appl. 60, No.1, 19-31 (1989). ISSN 0022-3239; ISSN 1573-2878/e

In this work, as usual in vector-valued optimization, we consider the partial ordering induced in a topological vector space by a closed and convex cone. In this way, we define maximal and minimal sets of a vector- valued function and consider minimax problems in this setting. Under suitable hypotheses (continuity, compactness, and special types of convexity), we prove that, for every $$ \alpha \in Max\cup \sb{s\in X\sb 0}Min\sb wf(s,Y\sb 0), $$ there exists $$ \beta \in Min\cup \sb{t\in Y\sb 0}Max f(X\sb 0,t) $$ such that $\beta\le \alpha$ (the exact meanings of the symbols are given in Section 2).

MSC 2000:: *90C31 Sensitivity, etc.

Keywords: vector-valued optimization; minimax problems

Cited in: Zbl 1054.90086 Zbl 0821.90136 Zbl 0696.90061

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Zentralblatt MATH Berlin [Germany]