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

Author

Listed:
  • Jean-Pierre Crouzeix

    (Université Clermont-Auvergne)

  • Abdelhak Hassouni

    (Université Mohammed 5)

  • Eladio Ocaña

    (Universidad Nacional de Ingeniería)

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.

Suggested Citation

  • Jean-Pierre Crouzeix & Abdelhak Hassouni & Eladio Ocaña, 2023. "A Short Note on the Twice Differentiability of the Marginal Function of a Convex Function," Journal of Optimization Theory and Applications, Springer, vol. 198(2), pages 857-867, August.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:2:d:10.1007_s10957-023-02267-4
    DOI: 10.1007/s10957-023-02267-4
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    References listed on IDEAS

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    1. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
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