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

Miglierina, E.; Molho, E.

Math. Methods Oper. Res. 58, No. 3, 375-385 (2003).

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

Keywords:

Vector optimization; Well-posedness; Stability; Hausdorff set-convergence