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A minimax theorem for vector-valued functions. (English) Zbl 0631.90077

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

αMax sX 0 Min w f(s,Y 0 ),

there exists

βMin tY 0 Maxf(X 0 ,t)

such that βα (the exact meanings of the symbols are given in Section 2).


MSC:
90C31Sensitivity, stability, parametric optimization
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