WEAKE-OPTIMAL SOLUTION IN VECTOR OPTIMIZATION

In a real locally convex Hausdorff topological vector space, we first introduce the concept of nearlyE-subconvexlikeness of set-valued maps via improvement set and obtain an alternative theorem. Furthermore, under the assumption of nearly subconvexlikeness, we establish scalarization theorem, Lagran...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 17; no. 4; pp. 1287 - 1302
Main Authors Zhao, Ke-Quan, Yang, Xin-Min, Peng, Jian-Wen
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.08.2013
Subjects
Convexity
Economic theory
Lagrange multipliers
Mathematical duality
Mathematical theorems
Mathematical vectors
Saddle points
Topological theorems
Topological vector spaces
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ISSN1027-5487
2224-6851

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Summary:In a real locally convex Hausdorff topological vector space, we first introduce the concept of nearlyE-subconvexlikeness of set-valued maps via improvement set and obtain an alternative theorem. Furthermore, under the assumption of nearly subconvexlikeness, we establish scalarization theorem, Lagrange multiplier theorem, weakE-saddle point criteria and weakE-duality for weakE-optimal solution in vector optimization with set-valued maps. We also propose some examples to illustrate the main results. 2010Mathematics Subject Classification: 90C26, 90C29, 90C30. Key words and phrases: Improvement set, WeakE-optimal solution, Scalarization, Lagrange multiplier, WeakE-saddle point, WeakE-duality, Vector optimization.
ISSN:1027-5487
2224-6851