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Second order analysis for robust inclusion systems and applications

Author

Listed:
  • V. D. Thinh

    (University of Science
    Vietnam National University
    Dong Thap University)

  • T. D. Chuong

    (Saigon University)

  • N. L. H. Anh

    (University of Science
    Vietnam National University)

Abstract

In this paper, we study an uncertain inequality system, where the input data are uncertain and belong to prescribed uncertainty sets. Using the deterministic approach in robust optimization, we treat this uncertain system by examining the so-called robust system. This approach enables us to compute the second order tangent sets for the solution set of the robust system and then obtain the second order epi-subderivative for the indicator function of its solution set. In this way, we are able to calculate the graphical derivative for the normal cone mapping of solution set of the robust system under certain qualification conditions. As applications, we establish second order necessary and sufficient optimality conditions, and derive necessary and sufficient conditions for stability properties such as the isolated calmness of optimization problems involving uncertain constraints under weak qualification conditions.

Suggested Citation

  • V. D. Thinh & T. D. Chuong & N. L. H. Anh, 2023. "Second order analysis for robust inclusion systems and applications," Journal of Global Optimization, Springer, vol. 85(1), pages 81-110, January.
    • Handle: RePEc:spr:jglopt:v:85:y:2023:i:1:d:10.1007_s10898-022-01197-1
    DOI: 10.1007/s10898-022-01197-1
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    References listed on IDEAS

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    1. Helmut Gfrerer & Jiří V. Outrata, 2016. "On Computation of Generalized Derivatives of the Normal-Cone Mapping and Their Applications," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1535-1556, November.
    2. Nguyen Thanh Qui, 2014. "Generalized Differentiation of a Class of Normal Cone Operators," Journal of Optimization Theory and Applications, Springer, vol. 161(2), pages 398-429, May.
    3. Thai Doan Chuong & Do Sang Kim, 2016. "Hölder-Like Property and Metric Regularity of a Positive-Order for Implicit Multifunctions," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 596-611, May.
    4. N. D. Yen, 1995. "Lipschitz Continuity of Solutions of Variational Inequalities with a Parametric Polyhedral Constraint," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 695-708, August.
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    Cited by:

    1. Thinh, Vo Duc & Chuong, Thai Doan & Le Hoang Anh, Nguyen, 2023. "Formulas of first-ordered and second-ordered generalization differentials for convex robust systems with applications," Applied Mathematics and Computation, Elsevier, vol. 455(C).

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