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Coercivity properties and well-posedness invector optimization*

Published online by Cambridge University Press:  15 December 2003

Sien Deng
Sien Deng*
Affiliation:
Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, USA; deng@math.niu.edu.
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Abstract

This paper studies the issue of well-posedness for vector optimization. It is shown that coercivity implies well-posedness without any convexity assumptions on problem data. For convex vector optimization problems, solution sets of such problems are non-convex in general, but they are highly structured. By exploring such structures carefully via convex analysis, we are able to obtain a number of positive results, including a criterion for well-posedness in terms of that of associated scalar problems. In particular we show that a well-known relative interiority condition can be used as a sufficient condition for well-posedness in convex vector optimization.

Keywords

Vector optimizationweakly efficient solutionwell posednesslevel-coercivityerror boundsrelative interior.
Type
Research Article
Information
RAIRO - Operations Research , Volume 37 , Issue 3 , July 2003 , pp. 195 - 208
Copyright
© EDP Sciences, 2003

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