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

Juan Liu (), Xian-Jun Long () and Xiang-Kai Sun ()
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Juan Liu: Chongqing Technology and Business University
Xian-Jun Long: Chongqing Technology and Business University
Xiang-Kai Sun: Chongqing Technology and Business University

Journal of Global Optimization, 2023, vol. 87, issue 2, No 8, 501 pages

Abstract: 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.

Keywords: Nonconvex uncertain semi-infinite programming; Tangential subdifferential; Robust optimal solution set; Dini pseudoconvexity; 90C26; 90C34; 90C46 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10898-022-01134-2

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