A Semismooth Newton-CG Augmented Lagrangian Method for Large Scale Linear and Convex Quadratic SDPS

Abstract

In this thesis, we introduce a semismooth Newton-CG augmented Lagrangian method for solving linear and convex quadratic semidefinite programming problems from the perspective of approximate semimsooth Newton methods. Under the framework of Euclidean Jordan algebras, we study the properties of these minimization problems and analyze the convergence of our proposed method. As a special case, based on the simple structure of linear symmetric cone programming and its dual, we characterize the Lipschitz continuity of the solution mapping for the dual problem at the origin. Numerical experiments on a variety of large scale convex linear and quadratic semidefinite programming show that the proposed method is very efficient.