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Block coordinate proximal gradient methods with variable Bregman functions for nonsmooth separable optimization.
- Source :
- Mathematical Programming; Nov2016, Vol. 160 Issue 1/2, p1-32, 32p
- Publication Year :
- 2016
-
Abstract
- In this paper, we propose a class of block coordinate proximal gradient (BCPG) methods for solving large-scale nonsmooth separable optimization problems. The proposed BCPG methods are based on the Bregman functions, which may vary at each iteration. These methods include many well-known optimization methods, such as the quasi-Newton method, the block coordinate descent method, and the proximal point method. For the proposed methods, we establish their global convergence properties when the blocks are selected by the Gauss-Seidel rule. Further, under some additional appropriate assumptions, we show that the convergence rate of the proposed methods is R-linear. We also present numerical results for a new BCPG method with variable kernels for a convex problem with separable simplex constraints. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00255610
- Volume :
- 160
- Issue :
- 1/2
- Database :
- Complementary Index
- Journal :
- Mathematical Programming
- Publication Type :
- Academic Journal
- Accession number :
- 118668986
- Full Text :
- https://doi.org/10.1007/s10107-015-0969-z