Two approaches toward constrained vector optimization and identity of the solutions

Crespi Giovanni P., Ginchev Ivan () and Rocca Matteo ()
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Crespi Giovanni P.: Department of Economics, University of Insubria, Italy
Ginchev Ivan: Department of Mathematics Varna, Bulgaria
Rocca Matteo: Department of Economics, University of Insubria, Italy

Economics and Quantitative Methods from Department of Economics, University of Insubria

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 double” 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 mostly under convexity type conditions. Key words: Constrained vector optimization, Optimality conditions, Stability, Type of solutions and their identity, Vector optimization and convexity type conditions.

Pages: 15 pages
Date: 2004-07
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