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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Published in | Optimization Vol. 64; no. 4; pp. 739 - 752 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Philadelphia
Taylor & Francis
03.04.2015
Taylor & Francis LLC |
Subjects | |
Online Access | Get full text |
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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. |
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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 0233-1934 1029-4945 |
DOI: | 10.1080/02331934.2013.798321 |