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Mordukhovich subgradients of the value function to a parametric discrete optimal control problem

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  • N. Toan
  • J.-C. Yao

Abstract

This paper is devoted to the study of the first-order behavior of the value function of a parametric discrete optimal control problem with nonconvex cost functions and control constraints. By establishing an abstract result on the Mordukhovich subdifferential of the value function of a parametric mathematical programming problem, we derive a formula for computing the Mordukhovich subdifferential of the value function to a parametric discrete optimal control problem. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:58:y:2014:i:3:p:595-612
    DOI: 10.1007/s10898-013-0062-1
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Zhaotong Lian & Liming Liu & Marcel F. Neuts, 2005. "A Discrete-Time Model for Common Lifetime Inventory Systems," Mathematics of Operations Research, INFORMS, vol. 30(3), pages 718-732, August.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

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