Pareto Well-Posedness for Set-Valued Optimization Problems in Geoffroy Spaces

James Larrouy ()
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James Larrouy: Université des Antilles

Journal of Optimization Theory and Applications, 2026, vol. 208, issue 1, No 20, 52 pages

Abstract: Abstract In this work, we study the well-posedness of set-valued optimization problems within a new topological conlinear structure called Geoffroy space. We first study the nonemptyness and the closedness of the set of Pareto minimal solutions. Then, we introduce three notions of well-posedness related to this class of minimal solutions and give some necessary and sufficient conditions ensuring the well-posedness of set-valued optimization problems. We conclude our study by applying our theoretical results to non-convex portfolio optimization problems arising in finance.

Keywords: Geoffroy space; Global well-posedness; Levitin-Polyak well-posedness; portfolio optimization; set optimization; 49J53; 49K40; 54A05; 90C29; 90C31 (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/s10957-025-02851-w

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