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S-Derivative of the Extremum Multifunction to a Multi-objective Parametric Discrete Optimal Control Problem

Author

Listed:
  • Nguyen Thi Toan

    (Hanoi University of Science and Technology)

  • Le Quang Thuy

    (Hanoi University of Science and Technology)

Abstract

In this paper, we derive formulae for computing the S-derivative of the extremum multifunction in a multi-objective parametric discrete optimal control problem with nonconvex objective functions and control constraints. Particularly, we obtain formulae for upper and lower evaluation on the S-derivative of the extremum multifunction via the solution of state equations, the tangent cone to the constraint sets, and the Fréchet derivative of the objective functions. By establishing an abstract result on the S-derivative of the extremum multifunction in a multi-objective parametric mathematical programming problem, we derive formulae for upper and lower evaluation on the S-derivative of the extremum multifunction in a multi-objective parametric discrete optimal control problem.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:196:y:2023:i:1:d:10.1007_s10957-022-02130-y
    DOI: 10.1007/s10957-022-02130-y
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    References listed on IDEAS

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