E-Benson proper efficiency in vector optimization

Starting from the innovative ideas of Chicco et al. (Vector optimization problems via improvement sets. J. Optim. Theory Appl. 2011;150:516-529), in this paper, the concepts of improvement set and -efficiency are introduced in a real locally convex Hausdorff topological vector space. Furthermore, so...

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Bibliographic Details
Published inOptimization Vol. 64; no. 4; pp. 739 - 752
Main Authors Zhao, Ke Quan, Yang, Xin Min
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.04.2015
Taylor & Francis LLC
Subjects
Approximation
Convex analysis
E-Benson proper efficiency
E-subconvexlikeness
Efficiency
Lagrange multiplier
Lagrange multipliers
Mathematical analysis
Mathematical problems
Optimization
scalarization
Studies
Theorems
Topology
vector optimization
Vector space
Vector spaces
Vectors (mathematics)
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Summary:Starting from the innovative ideas of Chicco et al. (Vector optimization problems via improvement sets. J. Optim. Theory Appl. 2011;150:516-529), in this paper, the concepts of improvement set and -efficiency are introduced in a real locally convex Hausdorff topological vector space. Furthermore, some properties of the improvement sets are given and a kind of proper efficiency, named as -Benson proper efficiency, which unifies some proper efficiency and approximate proper efficiency, is proposed via the improvement sets in vector optimization. Moreover, the concept of -subconvexlikeness of set-valued maps is introduced via the improvement sets and an alternative theorem is proved. In the end, some scalarization theorems and Lagrange multiplier theorems of -Benson proper efficiency are established for a vector optimization problem with set-valued maps.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2013.798321