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Characterizing robust optimal solution sets for nonconvex uncertain semi-infinite programming problems involving tangential subdifferentials

Author

Listed:
  • Juan Liu

    (Chongqing Technology and Business University)

  • Xian-Jun Long

    (Chongqing Technology and Business University)

  • Xiang-Kai Sun

    (Chongqing Technology and Business University)

Abstract

In this paper, we give some characterizations of the robust optimal solution set for nonconvex uncertain semi-infinite programming problems in terms of tangential subdifferentials. By using a new robust-type constraint qualification, we first obtain some necessary and sufficient optimality conditions of the robust optimal solution for the nonconvex uncertain semi-infinite programming problem via the robust optimization approach. Then, by using the Dini pseudoconvexity, we obtain some characterizations of the robust optimal solution set for the nonconvex uncertain semi-infinite programming problem. Finally, as applications of our results, we derive some optimality conditions of the robust optimal solution and characterizations of the robust optimal solution set for the cone-constrained nonconvex uncertain optimization problem. Some examples are given to illustrate the advantage of the results.

Suggested Citation

  • Juan Liu & Xian-Jun Long & Xiang-Kai Sun, 2023. "Characterizing robust optimal solution sets for nonconvex uncertain semi-infinite programming problems involving tangential subdifferentials," Journal of Global Optimization, Springer, vol. 87(2), pages 481-501, November.
  • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-022-01134-2
    DOI: 10.1007/s10898-022-01134-2
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    References listed on IDEAS

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    1. S. K. Mishra & B. B. Upadhyay & Le Thi Hoai An, 2014. "Lagrange Multiplier Characterizations of Solution Sets of Constrained Nonsmooth Pseudolinear Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 763-777, March.
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    5. Jiawei Chen & Elisabeth Köbis & Jen-Chih Yao, 2019. "Optimality Conditions and Duality for Robust Nonsmooth Multiobjective Optimization Problems with Constraints," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 411-436, May.
    6. V. Jeyakumar & G. M. Lee & G. Li, 2015. "Characterizing Robust Solution Sets of Convex Programs under Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 407-435, February.
    7. Xiangkai Sun & Kok Lay Teo & Liping Tang, 2019. "Dual Approaches to Characterize Robust Optimal Solution Sets for a Class of Uncertain Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 984-1000, September.
    8. J.P. Penot, 2003. "Characterization of Solution Sets of Quasiconvex Programs," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 627-636, June.
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