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Strong Vector Minimization and Duality
Author(s) -
Craven B. D.
Publication year - 1980
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19800600102
Subject(s) - strong duality , duality (order theory) , convexity , weak duality , perturbation function , mathematics , vector valued function , converse , wolfe duality , minification , duality gap , cone (formal languages) , dual space , dual (grammatical number) , pure mathematics , convex analysis , optimization problem , mathematical optimization , convex optimization , regular polygon , algorithm , geometry , financial economics , economics , art , literature
A constrained minimum of a vector valued function is defined, in terms of an ordering cone. The definition chosen leads to a vector analog of the Kuhn‐Tucker theorem, and to a duality theorem where the dual problem has a vector valued objective function, and weak duality is defined by appropriate cone orderings. Also proved are a vector valued converse duality theorem, and a vector quasiduality theorem which does not require convexity. The results are related to perturbations of the objective function in a minimization problem.