Abstract
We provide new characterizations of the \(\varepsilon \)-subdifferential of the supremum of an arbitrary family of convex functions. The resulting formulas only involve approximate subdifferentials of adequate convex combinations of the data functions. Families of convex functions with a concavity-like property are introduced and their relationship with affine models is studied. The role of the lower semi-continuity of the data functions is also analyzed.
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The authors are very grateful for the referees’ thorough reviews, which have definitely contributed to improving the latest version of the article.
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Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. The research of the first author is supported by Centro Basal CMM FB210005 and by Fondecyt Regular 1240335. Second and third authors are supported by the Research Project PID2022-136399NB-C21 from MICINN, Spain. The research of the second author is also supported by MICIU of Spain and Universidad de Alicante (Contract Beatriz Galindo BEA- GAL 18/00205), AICO/2021/165 of Generalitat Valenciana CMM FB210005.
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Correa, R., Hantoute, A. & López, M.A. Conjugation-Based Approach to the \(\varepsilon \)-Subdifferential of Convex Suprema. Set-Valued Var. Anal 32, 8 (2024). https://doi.org/10.1007/s11228-024-00712-8
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DOI: https://doi.org/10.1007/s11228-024-00712-8