Stability of KKT systems and superlinear convergence of the SQP method under parabolic regularity

TL;DR

This paper introduces new second-order stability characterizations for perturbed KKT systems in constrained optimization and demonstrates superlinear convergence of SQP methods under parabolic regularity.

Contribution

It provides novel second-order conditions for stability of KKT systems and applies these to prove superlinear convergence of SQP methods for parabolically regular problems.

Findings

New second-order stability characterizations for KKT systems

Superlinear convergence of SQP under parabolic regularity

Enhanced understanding of robustness in constrained optimization

Abstract

This paper pursues a two-fold goal. Firstly, we aim to derive novel second-order characterizations of important robust stability properties of perturbed Karush-Kuhn-Tucker systems for a broadclass of constrained optimization problems generated by parabolically regular sets. Secondly, the obtained characterizations are applied to establish well-posedness and superlinear convergence of the basic sequential quadratic programming method to solve parabolically regular constrained optimization problems.