Formulas of first-ordered and second-ordered generalization differentials for convex robust systems with applications

Vo Duc Thinh, Thai Doan Chuong and Nguyen Le Hoang Anh

Applied Mathematics and Computation, 2023, vol. 455, issue C

Abstract: In the paper, we start by establishing first and second-ordered analysis for a convex inequality system that contains uncertainty data, including calculating normal and tangent cones, second-ordered tangent sets for the solution set to this system, and first and second-ordered epi-subderivatives for the indicator function of its solution set. Then, we provide second-ordered necessary and sufficient optimality conditions for strict solutions of convex robust optimization problems. Moreover, an associated algorithm converging quickly to a solution for the class of quadratic robust optimization problems is proposed. The theoretical results are newly obtained under weak qualification conditions, and numerical examples show the advantage of the given method.

Keywords: Convex robust programming; Second-ordered tangent set; Epi-subderivative; Second-ordered epi-subderivative; Superlinear convergence; Semi-infinite programming (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:455:y:2023:i:c:s0096300323002837

DOI: 10.1016/j.amc.2023.128114

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