Miglierina, E.; Molho, E.; Rocca, M. Well-posedness and scalarization in vector optimization. (English) Zbl 1129.90346 J. Optim. Theory Appl. 126, No. 2, 391-409 (2005). Summary: In this paper, we study several existing notions of well- posedness for vector optimization problems. We separate them into two classes and we establish the hierarchical structure of their relationships. Moreover, we relate vector well-posedness and well-posedness of an appropriate scalarization. This approach allows us to show that, under some compactness assumption, quasiconvex problems are well posed. Cited in 61 Documents MSC: 90C29 Multi-objective and goal programming 90C31 Sensitivity, stability, parametric optimization 49K40 Sensitivity, stability, well-posedness PDF BibTeX XML Cite \textit{E. Miglierina} et al., J. Optim. Theory Appl. 126, No. 2, 391--409 (2005; Zbl 1129.90346) Full Text: DOI References: [15] Bednarczuck E. (1992). Some Stability Results for Vector Optimization Problems in Partially-Ordered Topological Vector Spaces, 1992 World Congress of Nonlinear Analysts, Tampa, Florida, 1992; de Gruyter, Berlin, Germany, pp. 2371–2382. [22] Gorokhovik V.V. (1990). Convex and Nonsmooth Optimization Problems of Vector Optimization, Nauka i Tékhnika, Minsk, Belarus, (in Russian). · Zbl 0765.90079 [27] Ginchev I., Guerraggio A., Rocca M. (1989). From Scalar to Vector Optimization, Applications of Mathematics (to appear) 28. Luc, D. T., Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Springer Verlag, Berlin, Germany, Vol. 319. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.