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