Two approaches toward constrained vector optimization and identity of the solutions

Giovanni P. Crespi; Ivan Ginchev; Matteo Rocca

doi:10.3934/jimo.2005.1.549

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2005, Volume 1, Issue 4: 549-563. Doi: 10.3934/jimo.2005.1.549

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Two approaches toward constrained vector optimization and identity of the solutions

1.
Université de la Vallée d'Aoste, Facoltà di Scienze Economiche, 11100 Aosta
2.
Technical University of Varna, Department of Mathematics, 9010 Varna
3.
University of Insubria, Department of Economics, 21100 Varese

Received: August 31, 2004

Revised: January 31, 2005

Published: September 2005

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Abstract

In this paper we deal with a Fritz John type constrained vector optimization problem. In spite that there are many concepts of solutions for an unconstrained vector optimization problem, we show the possibility ''to doubl'' the number of concepts when a constrained problem is considered. In particular we introduce sense I and sense II isolated minimizers, properly efficient points, efficient points and weakly efficient points. As a motivation leading to these concepts we give some results concerning optimality conditions in constrained vector optimization and stability properties of isolated minimizers and properly efficient points. Our main investigation and results concern relations between sense I and sense II concepts. These relations are proved often under convexity type conditions.

Keywords:

Constrained vector optimization,
optimality conditions,
stability,
type of solutions and their identity,
vector optimization and convexity type conditions.

Mathematics Subject Classification: Primary: 90C29.

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