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 \[ \alpha \in Max\cup _{s\in X_ 0}Min_ wf(s,Y_ 0), \] there exists \[ \beta \in Min\cup _{t\in Y_ 0}Max f(X_ 0,t) \] such that \(\beta\leq \alpha\) (the exact meanings of the symbols are given in Section 2).


90C31 Sensitivity, stability, parametric optimization
Full Text: DOI


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