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Approximately Efficient Solutions in Vector Optimization
Author(s) -
Tanaka Tamaki
Publication year - 1996
Publication title -
journal of multi‐criteria decision analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.462
H-Index - 47
eISSN - 1099-1360
pISSN - 1057-9214
DOI - 10.1002/(sici)1099-1360(199612)5:4<271::aid-mcda114>3.0.co;2-w
Subject(s) - vector optimization , cone (formal languages) , banach space , mathematics , regular polygon , set (abstract data type) , point (geometry) , convex cone , space (punctuation) , vector space , ordered vector space , locally convex topological vector space , conic optimization , convex optimization , optimization problem , convex set , property (philosophy) , mathematical optimization , mathematical analysis , pure mathematics , algorithm , computer science , geometry , multi swarm optimization , functional analysis , philosophy , operating system , epistemology , programming language , chemistry , interpolation space , biochemistry , gene
An approach to approximating solutions in vector optimization is developed for vector optimization problems with arbitrary ordering cones. This paper presents a study of approximately efficient points of a given set with respect to a convex cone in an ordered Banach space. Existence results for such approximately efficient points are obtained. A domination property related to these existence results is observed and then it is proved that each element of a given set is approximated by the sum of a point in a convex cone inducing the ordering and a point in a finite set consisting of such approximately efficient points of the set.