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New Tour on the Subdifferential of Supremum via Finite Sums and Suprema

Author

Listed:
  • A. Hantoute

    (Universidad de Alicante
    Universidad de Chile)

  • M. A. López-Cerdá

    (Universidad de Alicante
    CIAO, Federation University)

Abstract

This paper provides new characterizations for the subdifferential of the pointwise supremum of an arbitrary family of convex functions. The main feature of our approach is that the normal cone to the effective domain of the supremum (or to finite-dimensional sections of it) does not appear in our formulas. Another aspect of our analysis is that it emphasizes the relationship with the subdifferential of the supremum of finite subfamilies, or equivalently, finite weighted sums. Some specific results are given in the setting of reflexive Banach spaces, showing that the subdifferential of the supremum can be reduced to the supremum of a countable family.

Suggested Citation

  • A. Hantoute & M. A. López-Cerdá, 2022. "New Tour on the Subdifferential of Supremum via Finite Sums and Suprema," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 81-106, June.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-021-01925-9
    DOI: 10.1007/s10957-021-01925-9
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    References listed on IDEAS

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    1. A. Ioffe, 2012. "A note on subdifferentials of pointwise suprema," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 456-466, July.
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