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Subgradients of the Value Function in a Parametric Convex Optimal Control Problem

Author

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  • Le Quang Thuy

    (Hanoi University of Science and Technology)

  • Nguyen Thi Toan

    (Hanoi University of Science and Technology)

Abstract

Motivated by our recent works on the optimal value function in parametric optimal control problems under linear state equations, in this paper we study of the first-order behavior of the value function of a parametric convex optimal control problem with a convex cost function and linear state equations. By establishing an abstract result on the subdifferential of the value function to a parametric convex mathematical programming problem, we derive a formula for computing the subdifferential and the singular subdifferential of the value function to a parametric convex optimal control problem. By virtue of the convexity, several assumptions used in the above papers, like the existence of a local upper Lipschitzian selection of the solution map, as well as the V-inner semicontinuity of the solution map, are no longer needed.

Suggested Citation

  • Le Quang Thuy & Nguyen Thi Toan, 2016. "Subgradients of the Value Function in a Parametric Convex Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 43-64, July.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-016-0921-2
    DOI: 10.1007/s10957-016-0921-2
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    References listed on IDEAS

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    1. Boris S. Mordukhovich & Nguyen Mau Nam, 2005. "Variational Stability and Marginal Functions via Generalized Differentiation," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 800-816, November.
    2. N. H. Chieu & B. T. Kien & N. T. Toan, 2016. "Further Results on Subgradients of the Value Function to a Parametric Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 785-801, March.
    3. Alberto Seeger, 1996. "Subgradients of Optimal-Value Functions in Dynamic Programming: The Case of Convex Systems Without Optimal Paths," Mathematics of Operations Research, INFORMS, vol. 21(3), pages 555-575, August.
    4. 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.
    5. Kien, B.T. & Liou, Y.C. & Wong, N.-C. & Yao, J.-C., 2009. "Subgradients of value functions in parametric dynamic programming," European Journal of Operational Research, Elsevier, vol. 193(1), pages 12-22, February.
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    Cited by:

    1. Nguyen Thi Toan & Le Quang Thuy, 2023. "S-Derivative of the Extremum Multifunction to a Multi-objective Parametric Discrete Optimal Control Problem," Journal of Optimization Theory and Applications, Springer, vol. 196(1), pages 240-265, January.

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