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Stability Analysis to Parametric Multiobjective Optimal Control Problems

Author

Listed:
  • Lam Quoc Anh

    (Can Tho University)

  • Vo Thanh Tai

    (An Giang University
    Vietnam National University)

  • Tran Ngoc Tam

    (Can Tho University)

Abstract

In this paper, we investigate continuity properties of the efficient solution map of a parametric nonlinear multiobjective optimal control problem. First, by using the equimeasurability condition of the admissible control set, we obtain the compactness and arcwise connectedness of the feasible solution set. Next, we suggest new concepts of the quasi-arcwise connected integrand and employ them to study the semicontinuity of the efficient solution map of this problem. When the multiobjective function does not satisfy these conditions, we propose an estimation hypothesis for approximate efficient solutions to address lower semicontinuity conditions of the efficient solution map of the reference problem. To illustrate the applicability, we apply the obtained results to two practical models, including Glucose model and Epidemic model.

Suggested Citation

  • Lam Quoc Anh & Vo Thanh Tai & Tran Ngoc Tam, 2025. "Stability Analysis to Parametric Multiobjective Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 204(1), pages 1-32, January.
    • Handle: RePEc:spr:joptap:v:204:y:2025:i:1:d:10.1007_s10957-024-02584-2
    DOI: 10.1007/s10957-024-02584-2
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    References listed on IDEAS

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    1. C. Kaya & Helmut Maurer, 2014. "A numerical method for nonconvex multi-objective optimal control problems," Computational Optimization and Applications, Springer, vol. 57(3), pages 685-702, April.
    2. C. S. Lalitha & Prashanto Chatterjee, 2012. "Stability for Properly Quasiconvex Vector Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 492-506, November.
    3. G. P. Crespi & M. Papalia & M. Rocca, 2009. "Extended Well-Posedness of Quasiconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 285-297, May.
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