Stabilized SQP Method for Convex Piecewise Linear-Quadratic Composite Optimization Problems

Abstract

This paper addresses the local convergence analysis of the stabilized sequential quadratic programming method for a class of composite optimization problems with convex piecewise linear- quadratic (CPLQ) modeling functions. We demonstrate that an appropriate second-order sufficient condition (SOSC) -formulated for composite problems- alone is sufficient to guarantee local superlin- ear convergence of the primal-dual sequence generated by this method. Furthermore, we examine the relaxation of the SOSC and show that it can be replaced with a weaker noncriticality of the associated Lagrange multiplier, provided, the modeling function is polyhedral and a relative interior condition is satisfied. We also present counterexamples showing that the relative interior condition is indispensable and that this relaxation fails for general CPLQ modeling functions.