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Journal of Convex Analysis 24 (2017), No. 4, 1169--1196
Copyright Heldermann Verlag 2017

Stability of E-optimal Points for Sequences of Functions

Pirro Oppezzi
DIMA, UniversitÓ di Genova, Via Dodecaneso 35, 16146 Genova, Italy

Anna Rossi
DIME, UniversitÓ di Genova, Piazzale Kennedy - Pad.D, 16129 Genova, Italy

The main concern of this article is the stability of optimal points for sequences of functions under suitable assumptions about convergence of their epigraphs. The optimality is based on an improvement set given in the value space. Several theorems, obtained in two previous papers, about the existence and stability of optimal points related to sequences of sets in infinite dimensional spaces, are here used in the case of sequences of functions' images. Most part of the present results are new also in the case where the criteria of optimality is a cone or the spaces have finite dimension.

Keywords: Vector optimization, improvement sets, variational convergence, stability of optimal points.

MSC: 49J45, 49K40, 90C31

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