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An Interior Proximal Method in Vector Optimization

Kely D Villacorta (kelydvv***at***cos.ufrj.br)
Paulo Roberto Oliveira(poliveir***at***cos.ufrj.br)

Abstract: This paper studies the vector optimization problem of finding weakly ef- ficient points for maps from Rn to Rm, with respect to the partial order induced by a closed, convex, and pointed cone C ⊂ Rm, with nonempty inte- rior. We develop for this problem an extension of the proximal point method for scalar-valued convex optimization problem with a modified convergence sensing conditon that allows us to construct an interior proximal method for solving POV on nonpolyhedral set.

Keywords: Interior point methods, vector optimization, C−convex, positively lower semicontinouos.

Category 1: Other Topics (Multi-Criteria Optimization )


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Entry Submitted: 10/06/2009
Entry Accepted: 10/06/2009
Entry Last Modified: 10/06/2009

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