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Further on Inner Regularizations in Bilevel Optimization

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  • M. Beatrice Lignola

    (University of Naples Federico II, Napoli)

  • Jacqueline Morgan

    (University of Naples Federico II, Napoli)

Abstract

A crucial difficulty in pessimistic bilevel optimization is the possible lack of existence of exact solutions since marginal functions of the sup type may fail to be lower semicontinuous. So, to overcome this drawback, we have introduced, in Lignola and Morgan (J Optim Theory Appl 173(1):183–202, 2017), suitable inner regularizations of the lower level optimization problem together with relative viscosity solutions for the pessimistic bilevel problem. Here, we continue this research by considering new inner regularizations of the lower level optimization problem, which not necessarily satisfy the constraints but that are close to them, and by deriving an existence result of related viscosity solutions to the pessimistic bilevel problem.

Suggested Citation

  • M. Beatrice Lignola & Jacqueline Morgan, 2019. "Further on Inner Regularizations in Bilevel Optimization," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 1087-1097, March.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1438-7
    DOI: 10.1007/s10957-018-1438-7
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    References listed on IDEAS

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    1. M. Beatrice Lignola & Jacqueline Morgan, 2017. "Inner Regularizations and Viscosity Solutions for Pessimistic Bilevel Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 183-202, April.
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    Cited by:

    1. Francesco Cesarone & Lorenzo Lampariello & Davide Merolla & Jacopo Maria Ricci & Simone Sagratella & Valerio Giuseppe Sasso, 2023. "A bilevel approach to ESG multi-portfolio selection," Computational Management Science, Springer, vol. 20(1), pages 1-23, December.
    2. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2024. "Asymptotic behavior of subgame perfect Nash equilibria in Stackelberg games," Annals of Operations Research, Springer, vol. 336(3), pages 1573-1590, May.

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