NDLI: Quasi-Slater and Farkas--Minkowski Qualifications for Semi-infinite Programming with Applications

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Li, Chong Zhao, Xiaopeng Hu, Yaohua
Copyright Year	2013
Abstract	The well-known Farkas--Minkowski (FM) type qualification plays an important role in linear semi-infinite programming and has been extensively developed by many authors in establishing optimality conditions, duality, and stability for semi-infinite programming. In this paper, we introduce the concept of the quasi-Slater condition for a semi-infinite convex inequality system and present that the Slater type conditions imply the FM qualification under some appropriate continuity assumption of the set-valued mapping $i\mapsto f_i(x)$. Applying these relationships, we establish dual characterizations, both asymptotic and nonasymptotic, for set containment problems and provide some sufficient conditions for ensuring the strong Lagrangian duality and Farkas lemma.
Starting Page	2208
Ending Page	2230
Page Count	23
File Format	PDF
ISSN	10526234
DOI	10.1137/130911287
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	4
Volume Number	23
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2013-11-12
Access Restriction	Subscribed
Subject Keyword	Optimality conditions, duality Semi-infinite programming Approximation with constraints set containment characterization semi-infinite programming Farkas lemma strong Lagrangian duality Slater condition Convex programming FM qualification
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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