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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年9月29日

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  • James Larrouy

摘要

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.