Volume 37, Number 3, July-September 2003
|Page(s)||195 - 208|
|Published online||15 December 2003|
Coercivity properties and well-posedness in vector optimization*
Department of Mathematical Sciences, Northern Illinois University,
DeKalb, Illinois 60115, USA; firstname.lastname@example.org.
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.
Key words: Vector optimization / weakly efficient solution / well posedness / level-coercivity / error bounds / relative interior.
© EDP Sciences, 2003
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