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Optimal Control of an Evolution Problem Involving Time-Dependent Maximal Monotone Operators

Author

Listed:
  • Nesrine Bouhali

    (Université Mohammed Seddik Benyahia)

  • Dalila Azzam-Laouir

    (Université Mohammed Seddik Benyahia)

  • Manuel D. P. Monteiro Marques

    (Faculdade de Ciências da Universidade de Lisboa)

Abstract

We consider a control problem in a finite-dimensional setting, which consists in finding a minimizer for a standard functional defined by way of two continuous and bounded below functions and a convex function, where the control functions take values in a closed convex set and the state functions solve a differential system made up of a differential inclusion governed by a maximal monotone operator; and an ordinary differential equation with a Lipschitz mapping in the right-hand side. We first show the existence of a unique absolutely continuous solution of our system, by transforming it to a sole evolution differential inclusion, and then use a result from the literature. Secondly, we prove the existence of an optimal solution to our problem. The main novelties are: the presence of the time-dependent maximal monotone operators, which may depend as well as their domains on the time variable; and the discretization scheme for the approximation of the solution.

Suggested Citation

  • Nesrine Bouhali & Dalila Azzam-Laouir & Manuel D. P. Monteiro Marques, 2022. "Optimal Control of an Evolution Problem Involving Time-Dependent Maximal Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 59-91, July.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:1:d:10.1007_s10957-022-02009-y
    DOI: 10.1007/s10957-022-02009-y
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    References listed on IDEAS

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    1. Elimhan N. Mahmudov, 2018. "Optimization of Mayer Problem with Sturm–Liouville-Type Differential Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 345-375, May.
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