A minimax theorem for vector-valued functions. II
type: Item
instance of: scholarly article
title: A minimax theorem for vector-valued functions. II
zbMATH Open document ID: 0696.90061
DOI: 10.1007/BF00939934
published in: Journal of Optimization Theory and Applications
publication date: 1991-01-01T00:00:00Z
review text: We deal with the minimax problem relative to a vector-valued function f: \(X_ 0\times Y_ 0\to V\), where a partial ordering in the topological vector space V is induced by a closed and convex cone C. In the first part of this article [ibid. 60, No.1, 19-31 (1989; Zbl 0631.90077)], under suitable hypotheses, we proved that \[ Max\cup_{s\in X_ 0}Min_ wf(s,Y_ 0)\subset Min\cup_{t\in Y_ 0}Max f(X_ 0,t)+C; \] the exact meaning of the symbols is given in Section 2. In this work, we prove that, under a reasonable setting of hypotheses, the previous inclusion holds and also we have that \[ Min_ w\cup_{t\in Y_ 0}Max f(X_ 0,t)\subset Max\cup_{s\in X_ 0}Min_ wf(s,Y_ 0)-C. \]
Mathematics Subject Classification ID: 90C29
Mathematics Subject Classification ID: 49J35
Mathematics Subject Classification ID: 46A99
Mathematics Subject Classification ID: 49J52
Mathematics Subject Classification ID: 90C48
zbMATH DE Number: 4141810
zbMATH Keywords: minimax problem
zbMATH Keywords: vector-valued function
zbMATH Keywords: topological vector space
zbMATH Keywords: closed and convex cone
author: Francesco Ferro
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00939934
OpenAlex ID: W2046362811
description: scientific article; zbMATH DE number 4141810