On the density of positive proper efficient points in a normed space
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AbstractIn the context of vector optimization and generalizing cones with bounded bases, we introduce and study quasi-Bishop-Phelps cones in a normed space X. A dual concept is also presented for the dual space X*. Given a convex subset A of a normed space X partially ordered by a closed convex cone S with a base, we show that, if A is weakly compact, then positive proper efficient points are sequentially weak dense in the set E( A, S) of efficient points of A; in particular, the connotation weak dense in the above can be replaced by the connotation norm dense if S is a quasi-Bishop-Phelps cone. Dually, for a convex subset of X* partially ordered by the dual cone S+, we establish some density results of positive weak* efficient elements of A in E(A, S+).
All Author(s) ListNg KF, Zheng XY
Journal nameJournal of Optimization Theory and Applications
Year2003
Month10
Day1
Volume Number119
Issue Number1
PublisherKLUWER ACADEMIC/PLENUM PUBL
Pages105 - 122
ISSN0022-3239
eISSN1573-2878
LanguagesEnglish-United Kingdom
Keywordsefficient points; normed spaces; positive proper efficient points; quasi-Bishop-Phelps cones; vector optimization
Web of Science Subject CategoriesMathematics; Mathematics, Applied; MATHEMATICS, APPLIED; Operations Research & Management Science; OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Last updated on 2020-24-10 at 02:05