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Sorin-Mihai Grad, Emilia-Loredana Pop: Vector duality for convex vector optimization problems with respect to quasi-minimality

Sorin-Mihai Grad, Emilia-Loredana Pop: Vector duality for convex vector optimization problems with respect to quasi-minimality

Author(s):
Sorin-Mihai Grad
Emilia-Loredana Pop
Title:
Sorin-Mihai Grad, Emilia-Loredana Pop: Vector duality for convex vector optimization problems with respect to quasi-minimality
Electronic source:
application/pdf
Preprint series:
Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 17, 2012
Mathematics Subject Classification:
49N15 []
90C25 []
90C29 []
Abstract:
We define the quasi-minimal elements of a set with respect to a convex cone and characterize them via linear scalarization. Then we attach to a general vector optimization problem a dual vector optimization problem with respect to quasi-efficient solutions and establish new duality results. By considering particular cases of the primal vector optimization problem we derive vector dual problems with respect to quasi-efficient solutions for both constrained and unconstrained vector optimization problems and the corresponding weak, strong and converse duality statements.
Keywords:
quasi-interior, quasi-minimal element, quasi-efficient solution, vector duality
Language:
English
Publication time:
12/2012