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A Weak Maximum Principle for Discrete Optimal Control Problems with Mixed Constraints

Author

Listed:
  • Roberto Andreani

    (State University of Campinas (Unicamp))

  • John Frank Matos Ascona

    (State University of Mato Grosso (UNEMAT))

  • Valeriano Antunes Oliveira

    (São Paulo State University (UNESP))

Abstract

In this study, first-order necessary optimality conditions, in the form of a weak maximum principle, are derived for discrete optimal control problems with mixed equality and inequality constraints. Such conditions are achieved by using the Dubovitskii–Milyutin formalism approach. Nondegenerate conditions are obtained under the constant rank of the subspace component (CRSC) constraint qualification, which is an important generalization of both the Mangasarian–Fromovitz and constant rank constraint qualifications. Beyond its theoretical significance, CRSC has practical importance because it is closely related to the formulation of optimization algorithms. In addition, an instance of a discrete optimal control problem is presented in which CRSC holds while other stronger regularity conditions do not.

Suggested Citation

  • Roberto Andreani & John Frank Matos Ascona & Valeriano Antunes Oliveira, 2024. "A Weak Maximum Principle for Discrete Optimal Control Problems with Mixed Constraints," Journal of Optimization Theory and Applications, Springer, vol. 203(1), pages 562-599, October.
    • Handle: RePEc:spr:joptap:v:203:y:2024:i:1:d:10.1007_s10957-024-02524-0
    DOI: 10.1007/s10957-024-02524-0
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    References listed on IDEAS

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    1. Le Quang Thuy & Bui Thi Thanh & Nguyen Thi Toan, 2017. "On the No-Gap Second-Order Optimality Conditions for a Discrete Optimal Control Problem with Mixed Constraints," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 421-442, May.
    2. N. T. Toan & Q. H. Ansari & J.-C. Yao, 2015. "Second-Order Necessary Optimality Conditions for a Discrete Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 165(3), pages 812-836, June.
    3. P. R. Kleindorfer & C. H. Kriebel & G. L. Thompson & G. B. Kleindorfer, 1975. "Discrete Optimal Control of Production Plans," Management Science, INFORMS, vol. 22(3), pages 261-273, November.
    4. Marko Antonio Rojas-Medar & Camila Isoton & Lucelina Batista Santos & Violeta Vivanco-Orellana, 2020. "Optimality Conditions for Discrete-Time Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 115-133, April.
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