2023/11/16 by Wei Zhou, Michel Théra, Wei, Zhou +3 · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Mathematical Inequalities and Applications #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2311.09884
openalex publication_date 2023/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Error bounds are central objects in optimization theory and its applications. They were for a long time restricted only to the theory before becoming over the course of time a field of itself. This paper is devoted to the study of error bounds of a general inequality defined by a proper lower semicontinuous function on an Asplund space. Even though the results of the dual characterization on the error bounds of a general inequality (if one drops the convexity assumption) may not be valid, several necessary dual conditions are still obtained in terms of Fréchet/Mordukhovich subdifferentials of the concerned function at points in the solution set. Moreover, for an inequality defined by a composite-convex function that is to say by a function which is the composition of a convex function with a smooth mapping, such dual conditions also turn out to be sufficient to have the error bound property. Our work is an extension of results on dual characterizations of convex inequalities to the possibly non-convex case.