Set-Valued Systems with Infinite-Dimensional Image and Applications

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 condit...

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Vydáno v:Journal of optimization theory and applications Ročník 179; číslo 3; s. 868 - 895
Hlavní autoři: Li, J., Yang, L.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.12.2018
Springer Nature B.V
Témata:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Engineering
Equivalence
Lagrangian function
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Saddle points
Separation
Theory of Computation
90C46
Set-valued mapping
90C29
Image space analysis
Quasi-relative interior
Generalized system
Saddle point
ISSN:0022-3239, 1573-2878
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-016-1041-8