In this paper, we provide two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex symmetric and nonsymmetric matrix optimization problems regularized by nonsmooth spectral functions. These sufficient conditions are derived via the study of the C2-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.
|Original language||English (US)|
|Number of pages||24|
|Journal||SIAM Journal on Optimization|
|State||Published - 2017|
Bibliographical noteFunding Information:
The research of the second author was supported by the National Natural Science Foundation of China under projects 11671387 and 11531014. The work of the third author was supported by the Youth Program of the National Natural Science Foundation of China under project 11101016.
© 2017 Society for Industrial and Applied Mathematics.
- Augmented Lagrangian function
- Fast convergence rates
- Matrix optimization
- Metric subregularity
- Quadratic growth conditions
- Spectral functions