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Further Results on Subgradients of the Value Function to a Parametric Optimal Control Problem

Author

Listed:
  • N. H. Chieu

    (Vinh University)

  • B. T. Kien

    (Hanoi National University of Civil Engineering)

  • N. T. Toan

    (Vinh University)

Abstract

This paper studies the first-order behavior of the value function of a parametric optimal control problem with nonconvex cost functions and control constraints. By establishing an abstract result on the Fréchet subdifferential of the value function of a parametric minimization problem, we derive a formula for computing the Fréchet subdifferential of the value function to a parametric optimal control problem. The obtained results improve and extend some previous results.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:3:d:10.1007_s10957-011-9933-0
    DOI: 10.1007/s10957-011-9933-0
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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. 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.
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    Cited by:

    1. 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.

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