Coercivity properties and well-posedness in vector optimization

Deng, Sien

RAIRO - Operations Research - Recherche Opérationnelle, Tome 37 (2003) no. 3, pp. 195-208.

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.

Mots clés : vector optimization, weakly efficient solution, well posedness, level-coercivity, error bounds, relative interior

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