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Well-posedness and convexity in vector optimization. (English) Zbl 1083.90036

Summary: We study a notion of well-posedness in vector optimization through the behaviour of minimizing sequences of sets, defined in terms of Hausdorff set-convergence. We show that the notion of strict efficiency is related to the notion of well-posedness. Using the obtained results we identify a class of well-posed vector optimization problems: the convex problems with compact efficient frontiers.

MSC:

90C29 Multi-objective and goal programming
90C31 Sensitivity, stability, parametric optimization
49K40 Sensitivity, stability, well-posedness
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