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Random Multifunctions as Set Minimizers of Infinitely Many Differentiable Random Functions

Author

Listed:
  • Juan Guillermo Garrido

    (Universidad de Chile
    Universidad de O’Higgins)

  • Pedro Pérez-Aros

    (Universidad de O’Higgins)

  • Emilio Vilches

    (Universidad de O’Higgins)

Abstract

Under mild assumptions, we prove that any random multifunction can be represented as the set of minimizers of an infinitely many differentiable normal integrand, which preserves the convexity of the random multifunction. This result is an extended random version of work done by Azagra and Ferrera (Proc Am Math Soc 130(12):3687–3692, 2002). We provide several applications of this result to the approximation of random multifunctions and integrands. The paper ends with a characterization of the set of integrable selections of a measurable multifunction as the set of minimizers of an infinitely many differentiable integral function.

Suggested Citation

  • Juan Guillermo Garrido & Pedro Pérez-Aros & Emilio Vilches, 2023. "Random Multifunctions as Set Minimizers of Infinitely Many Differentiable Random Functions," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 86-110, July.
    • Handle: RePEc:spr:joptap:v:198:y:2023:i:1:d:10.1007_s10957-023-02240-1
    DOI: 10.1007/s10957-023-02240-1
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    References listed on IDEAS

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    1. Didier Aussel & Anton Svensson, 2019. "Is Pessimistic Bilevel Programming a Special Case of a Mathematical Program with Complementarity Constraints?," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 504-520, May.
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