Abstract
In this paper, we provide some gentle introductions to the recent advance in augmented Lagrangian methods for solving large-scale convex matrix optimization problems (cMOP). Specifically, we reviewed two types of sufficient conditions for ensuring the quadratic growth conditions of a class of constrained convex matrix optimization problems regularized by nonsmooth spectral functions. Under a mild quadratic growth condition on the dual of cMOP, we further discussed the R-superlinear convergence of the Karush–Kuhn–Tucker (KKT) residuals of the sequence generated by the augmented Lagrangian methods (ALM) for solving convex matrix optimization problems. Implementation details of the ALM for solving core convex matrix optimization problems are also provided.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 305-342 |
| Number of pages | 38 |
| Journal | Journal of the Operations Research Society of China |
| Volume | 10 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jun 2022 |
Bibliographical note
Publisher Copyright:© 2021, Operations Research Society of China, Periodicals Agency of Shanghai University, Science Press, and Springer-Verlag GmbH Germany, part of Springer Nature.
Keywords
- Augmented Lagrangian methods
- Fast convergence rates
- Matrix optimization
- Metric subregularity
- Quadratic growth conditions
- Semismooth Newton methods
- Spectral functions
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