# American Institute of Mathematical Sciences

October  2005, 1(4): 549-563. doi: 10.3934/jimo.2005.1.549

## Two approaches toward constrained vector optimization and identity of the solutions

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

Received  September 2004 Revised  February 2005 Published  October 2005

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.
Citation: Giovanni P. Crespi, Ivan Ginchev, Matteo Rocca. Two approaches toward constrained vector optimization and identity of the solutions. Journal of Industrial and Management Optimization, 2005, 1 (4) : 549-563. doi: 10.3934/jimo.2005.1.549
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