Set-Valued Systems with Infinite-Dimensional Image and Applications

J. Li () and L. Yang ()
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J. Li: China West Normal University
L. Yang: China West Normal University

Journal of Optimization Theory and Applications, 2018, vol. 179, issue 3, No 7, 868-895

Abstract: Abstract In infinite-dimensional spaces, we investigate a set-valued system from the image perspective. By exploiting the quasi-interior and the quasi-relative interior, we give some new equivalent characterizations of (proper, regular) linear separation and establish some new sufficient and necessary conditions for the impossibility of the system under new assumptions, which do not require the set to have nonempty interior. We also present under mild assumptions the equivalence between (proper, regular) linear separation and saddle points of Lagrangian functions for the system. These results are applied to obtain some new saddle point sufficient and necessary optimality conditions of vector optimization problems.

Keywords: Image space analysis; Generalized system; Set-valued mapping; Quasi-relative interior; Saddle point; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-016-1041-8

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