Stability Analysis for Composite Optimization Problems and Parametric Variational Systems

TL;DR

This paper explores the stability properties of composite optimization problems and variational systems, linking full stability of minimizers with strong regularity of KKT systems and analyzing Lipschitzian stability in parametric settings.

Contribution

It establishes new relationships between full stability and strong regularity, and extends stability analysis to parametric variational systems with convex piecewise linear potentials.

Findings

Full stability relates to Robinson's strong regularity.

Lipschitzian stability of parametric systems is characterized.

Applications to second-order variational analysis are provided.

Abstract

This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of local minimizers in composite optimization and Robinson's strong regularity of associated (linearized and nonlinearized) KKT systems. Finally, we address Lipschitzian stability of parametric variational systems with convex piecewise linear potentials.