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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 $$ \alpha \in Max\cup \sb{s\in X\sb 0}Min\sb wf(s,Y\sb 0), $$ 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).

90C31Sensitivity, stability, parametric optimization
Full Text: DOI
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