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A Variational Approach to the Maximization of Preferences Without Numerical Representation

Author

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  • Monica Milasi

    (University of Messina)

  • Domenico Scopelliti

    (University of Messina
    University of Pavia)

Abstract

We introduce a variational approach to study a maximization problem of preferences that cannot be represented by a utility function. In such conditions, we reformulate the problem as a suitable variational problem and we give regularity properties of the solutions map. The theoretical results are applied in studying an equilibrium problem under uncertainty.

Suggested Citation

  • Monica Milasi & Domenico Scopelliti, 2021. "A Variational Approach to the Maximization of Preferences Without Numerical Representation," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 879-893, September.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:3:d:10.1007_s10957-021-01911-1
    DOI: 10.1007/s10957-021-01911-1
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    References listed on IDEAS

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    Cited by:

    1. Elisabetta Allevi & Didier Aussel & Rossana Riccardi & Domenico Scopelliti, 2024. "Single-Leader-Radner-Equilibrium: A New Approach for a Class of Bilevel Problems Under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 200(1), pages 344-370, January.
    2. Domenico Scopelliti, 2022. "On a Class of Multistage Stochastic Hierarchical Problems," Mathematics, MDPI, vol. 10(21), pages 1-13, October.
    3. Orestes Bueno & John Cotrina & Yboon García, 2023. "Existence and Uniqueness of Maximal Elements for Preference Relations: Variational Approach," Journal of Optimization Theory and Applications, Springer, vol. 198(3), pages 1246-1263, September.

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