Perturbation analysis of a class of composite optimization problems

Journal:Journal of the London Mathematical Society

Abstract:In this paper, we conduct a perturbation analysis of a class of composite optimization problems, providing a unified framework for addressing both theoretical and algorithmic aspects of constrained optimization problems. By exploiting the properties of the graphical derivative, limiting/Mordukhovich coderivative, and regular coderivative, we establish a strong second-order sufficient condition (SSOSC) for the composite optimization problem. This condition represents a novel contribution that cannot be directly inferred from existing definitions tailored to specific problems. Under certain mild assumptions on the objective function, it is demonstrated that SSOSC together with the nondegeneracy condition, the nonsingularity of Clarke's generalized Jacobian of the nonsmooth system at a Karush–Kuhn–Tucker (KKT) point, and strong regularity of the KKT point are equivalent. These findings provide a robust analytical tool for evaluating the stability of the KKT point.

First Author:Peipei Tang

Correspondence Author:Chengjing Wang

Discipline:Science

Volume:113

Issue:6

Page Number:1-29

Translation or Not:no

Date of Publication:2026-05-26

Included Journals:SCI

Links to published journals:https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/jlms.70580