Coercivity properties and well-posedness in vector optimization

Issue		RAIRO Oper. Res. Volume 37, Number 3, July-September 2003


Page(s)		195 - 208
DOI		10.1051/ro:2003021

RAIRO Oper. Res. 37 (2003) 195-208
DOI: 10.1051/ro:2003021

Coercivity properties and well-posedness in vector optimization

Sien Deng

Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115, USA; deng@math.niu.edu.. This research is supported in part by an Northern Illinois University internal grant.
(Received July, 2003.)

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.

Key words: Vector optimization, weakly efficient solution, well posedness, level-coercivity, error bounds, relative interior.

© EDP Sciences 2003

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