Optimality conditions for vector equilibrium problems  and their applications

Adela Capătă

doi:10.3934/jimo.2013.9.659

Article Contents

2013, Volume 9, Issue 3: 659-669. Doi: 10.3934/jimo.2013.9.659

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Optimality conditions for vector equilibrium problems and their applications

Adela Capătă^1,

1.
Technical University of Cluj-Napoca, Department of Mathematics, Str. G. Bariţiu 25, 400027, Cluj-Napoca

Received: November 30, 2011

Revised: February 28, 2013

Published: June 2013

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Abstract

The purpose of this paper is to establish necessary and sufficient conditions for a point to be solution of a vector equilibrium problem with cone and affine constraints. Using a separation theorem, which involves the quasi-interior of a convex set, we obtain optimality conditions for solutions of the vector equilibrium problem. Then, the main result is applied to vector optimization problems with cone and affine constraints and to duality theory.

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Mathematics Subject Classification: Primary: 90C46; Secondary: 49K35.

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