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Differential Stability Properties of Convex Optimization and Optimal Control Problems

Author

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  • Nguyen Thi Toan

    (Hanoi University of Science and Technology)

  • Le Quang Thuy

    (Hanoi University of Science and Technology)

Abstract

This paper studies the solution stability of convex optimization and discrete convex optimal control problems in Banach spaces, where the solution set may be empty. For both the optimization problem and the optimal control problem, formulas for the $$\varepsilon $$ ε -subdifferential of the optimal value function are derived without qualification conditions. We first calculate the $$\varepsilon $$ ε -subdifferential of the optimal value function to a parametric optimization problem with geometrical and functional constraints. We then use the obtained results to derive a formula for computing the $$\varepsilon $$ ε -subdifferential of the optimal value function to a discrete convex optimal control problem with linear state equations, control constraints and initial, terminal conditions.

Suggested Citation

  • Nguyen Thi Toan & Le Quang Thuy, 2024. "Differential Stability Properties of Convex Optimization and Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 201(2), pages 609-630, May.
    • Handle: RePEc:spr:joptap:v:201:y:2024:i:2:d:10.1007_s10957-024-02400-x
    DOI: 10.1007/s10957-024-02400-x
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    References listed on IDEAS

    as
    1. Duong Thi Viet An & Jen-Chih Yao, 2016. "Further Results on Differential Stability of Convex Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 28-42, July.
    2. N. Toan & J.-C. Yao, 2014. "Mordukhovich subgradients of the value function to a parametric discrete optimal control problem," Journal of Global Optimization, Springer, vol. 58(3), pages 595-612, March.
    Full references (including those not matched with items on IDEAS)

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