Convergence of the minimal sets under convexity in vector optimization

Miglierina Enrico and Molho Elena
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Miglierina Enrico: Department of Economics, University of Insubria, Italy
Molho Elena: University of Pavia, Italy

Economics and Quantitative Methods from Department of Economics, University of Insubria

Abstract: We study the behaviour of the minimal sets of a sequence of convex sets An converging to a given set A. Under suitable assumptions involving only the structure of the single sets An, we obtain the lower convergence of MinAn to MinA. In a reflexive Banach space ordered by a closed convex cone with a weakly compact base, we consider a sequence of convex sets An Mosco-converging to a set A. In the more general setting of a normed linear space ordered by a closed convex based cone (without any assumptions on the compactness of the base), we consider the stronger notion of Attouch-Wets convergence of the sequence of convex sets An. We compare our theorems with existing results related to the same topic.

Keywords: Stability; vector optimization; set-convergences; convexity (search for similar items in EconPapers)
Pages: 17 pages
Date: 2003-01
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Persistent link: https://EconPapers.repec.org/RePEc:ins:quaeco:qf0302

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