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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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