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A Short Note on the Twice Differentiability of the Marginal Function of a Convex Function

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Abstract

The main result concerns the second-order differentiability of the marginal function of a convex twice differentiable function. The inf-convolution and the proximal algorithm are revised according to the result as examples.

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Author information

Authors and Affiliations

  1. LIMOS, Université Clermont-Auvergne, 1 Rue de la Chebarde, 63178, Aubière, France

    Jean-Pierre Crouzeix

  2. Faculté des Sciences, Université Mohammed 5, B.P. 1014, Rabat, Morocco

    Abdelhak Hassouni

  3. IMCA, Instituto de Matemática y Ciencias Afines, Universidad Nacional de Ingeniería, Calle Los Biólogos 245 Urb. San César, La Molina, Lima 12, Peru

    Eladio Ocaña

Authors
  1. Jean-Pierre Crouzeix
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  2. Abdelhak Hassouni
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  3. Eladio Ocaña
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Corresponding author

Correspondence to Eladio Ocaña.

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Communicated by Nicolas-Hadjisavvas.

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Crouzeix, JP., Hassouni, A. & Ocaña, E. A Short Note on the Twice Differentiability of the Marginal Function of a Convex Function. J Optim Theory Appl 198, 857–867 (2023). https://doi.org/10.1007/s10957-023-02267-4

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  • DOI: https://doi.org/10.1007/s10957-023-02267-4

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