A minimax theorem for vector-valued functions

  • F. Ferro
Contributed Papers

Abstract

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
$$\alpha \varepsilon Max\bigcup\limits_{s\varepsilon X_o } {Min_w } f(s,Y_0 ),$$
there exists
$$\beta \varepsilon Min\bigcup\limits_{r\varepsilon Y_o } {Max} f(X_0 ,t),$$
such that β ≤ α (the exact meanings of the symbols are given in Section 2).

Key Words

Minimax theorems vector-valued optimization 

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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • F. Ferro
    • 1
  1. 1.Dipartimento di MatematicaUniversitá di GenovaGenovaItaly

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