Quadratic growth conditions for convex matrix optimization problems associated with spectral functions

Abstract

In this paper, we provide two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex symmetric and non-symmetric matrix optimization problems regularized by nonsmooth spectral functions. These sufficient conditions are derived via the study of the ${\mathcal{C}}^2$-cone reducibility of spectral functions and the metric subregularity of their subdifferentials, respectively. As an application, we demonstrate how quadratic growth conditions are used to guarantee the desirable fast convergence rates of the augmented Lagrangian methods (ALM) for solving convex matrix optimization problems. Numerical experiments on an easy-to-implement ALM applied to the fastest mixing Markov chain problem are also presented to illustrate the significance of the obtained results.

24 pages

References in corpus (4)

• Linear Rate Convergence of the Alternating Direction Method of Multipliers for Convex Composite Quadratic and Semi-Definite Programming
• On the Asymptotic Superlinear Convergence of the Augmented Lagrangian Method for Semidefinite Programming with Multiple Solutions
• QSDPNAL: A two-phase augmented Lagrangian method for convex quadratic semidefinite programming
• Critical Multipliers in Variational Systems via Second-order Generalized Differentiation

Cited by in corpus (1)

• Critical Multipliers in Semidefinite Programming