Coderivatives with respect to a set of the normal cone mappings and their applications

2023/12/26 by Vo Duc Thinh, Thinh, Vo Duc, Xiaolong Qin +3
Computer Science · Mathematics · #49J53 #90C30 #90C31 #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations #Optimization and Control (math.OC) #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2312.15834

openalex publication_date 2023/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Establishing explicit formulas of coderivatives with respect to a set of the normal cone mapping to a polyhedron, the solution set of a variational inequalities system, is one of the main goals of this paper. By using our coderivative formulas, we provide a characteristic of the Aubin property with respect to a set of that normal cone mapping and thereby give necessary optimality conditions for simple bilevel optimization problems under weak qualification conditions.

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