Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems
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arXiv
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| Natura: | Preprint |
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2019
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| _version_ | 1866909170746261504 |
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| author | Latafat, Puya Themelis, Andreas Patrinos, Panagiotis |
| author_facet | Latafat, Puya Themelis, Andreas Patrinos, Panagiotis |
| contents | This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the forward-backward envelope (FBE), which serves as a particularly suitable continuous and real-valued Lyapunov function. Global and linear convergence results are established when the cost function satisfies the Kurdyka-Łojasiewicz property without imposing convexity requirements on the smooth function. Two prominent special cases of the investigated setting are regularized finite sum minimization and the sharing problem; in particular, an immediate byproduct of our analysis leads to novel convergence results and rates for the popular Finito/MISO algorithm in the nonsmooth and nonconvex setting with very general sampling strategies. This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the forward-backward envelope (FBE), which serves as a particularly suitable continuous and real-valued Lyapunov function. Global and linear convergence results are established when the cost function satisfies the Kurdyka-Łojasiewicz property without imposing convexity requirements on the smooth function. Two prominent special cases of the investigated setting are regularized finite sum minimization and the sharing problem; in particular, an immediate byproduct of our analysis leads to novel convergence results and rates for the popular Finito/MISO algorithm in the nonsmooth and nonconvex setting with very general sampling strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_10053 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems Latafat, Puya Themelis, Andreas Patrinos, Panagiotis Optimization and Control 90C06, 90C25, 90C26, 49J52, 49J53 This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the forward-backward envelope (FBE), which serves as a particularly suitable continuous and real-valued Lyapunov function. Global and linear convergence results are established when the cost function satisfies the Kurdyka-Łojasiewicz property without imposing convexity requirements on the smooth function. Two prominent special cases of the investigated setting are regularized finite sum minimization and the sharing problem; in particular, an immediate byproduct of our analysis leads to novel convergence results and rates for the popular Finito/MISO algorithm in the nonsmooth and nonconvex setting with very general sampling strategies. This paper analyzes block-coordinate proximal gradient methods for minimizing the sum of a separable smooth function and a (nonseparable) nonsmooth function, both of which are allowed to be nonconvex. The main tool in our analysis is the forward-backward envelope (FBE), which serves as a particularly suitable continuous and real-valued Lyapunov function. Global and linear convergence results are established when the cost function satisfies the Kurdyka-Łojasiewicz property without imposing convexity requirements on the smooth function. Two prominent special cases of the investigated setting are regularized finite sum minimization and the sharing problem; in particular, an immediate byproduct of our analysis leads to novel convergence results and rates for the popular Finito/MISO algorithm in the nonsmooth and nonconvex setting with very general sampling strategies. |
| title | Block-coordinate and incremental aggregated proximal gradient methods for nonsmooth nonconvex problems |
| topic | Optimization and Control 90C06, 90C25, 90C26, 49J52, 49J53 |
| url | https://arxiv.org/abs/1906.10053 |