A newton-CG augmented Lagrangian method for convex quadratically constrained quadratic semidefinite programs

Abstract

This paper presents a Newton-CG augmented Lagrangian method for solving convex quadratically constrained quadratic semidefinite programming (QCQSDP) problems. Based on the Robinson’s CQ, the strong second order sufficient condition, and the constraint nondegeneracy conditions, we analyze the global convergence of the proposed method. For the inner problems, we prove the equivalence between the positive definiteness of the generalized Hessian of the objective functions in those inner problems and the constraint nondegeneracy of the corresponding dual problems, which guarantees the superlinear convergence of the inexact semismooth Newton-CG method to solve the inner problem. Numerical experiments show that the proposed method is very efficient to solve the large-scale convex QCQSDP problems.