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A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
Abstract
We consider the forward-backward splitting method for finding a zero of the sum of two maximal monotone mappings. This method is known to converge when the inverse of the forward mapping is strongly monotone. We propose a modification to this method, in the spirit of the extragradient method for monotone variational inequalities, under which the method converges assuming only the forward mapping is (Lipschitz) continuous on some closed convex subset of its domain. The modification entails an additional forward step and a projection step at each iteration. Applications of the modified method to decomposition in convex programming and monotone variational inequalities are discussed.
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Cited by
Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075
Boyd, S. (2010) · now publishers, Inc. eBooks · doi:10.1561/9781601984616 · Cited by 12,677
Parikh, N., & Boyd, S. (2014) · Foundations and Trends® in Optimization · doi:10.1561/2400000003 · Cited by 4,102
Fixed-Point Continuation for $\ell_1$-Minimization: Methodology and Convergence
Hale, E. T., Yin, W., & Zhang, Y. (2008) · SIAM Journal on Optimization · doi:10.1137/070698920 · Cited by 909
A Proximal Stochastic Gradient Method with Progressive Variance Reduction
Xiao, L., & Zhang, T. (2014) · SIAM Journal on Optimization · doi:10.1137/140961791 · Cited by 592
Metadata
- Authors
- Tseng, P.
- Venue
- SIAM Journal on Control and Optimization
- Published
- 2000-01
- Volume
- 38
- Issue
- 2
- Pages
- 431-446
- ISSN
- 0363-0129 (ISSN-L)
- 1095-7138
- OpenAlex
- W2055467852
- Cited by
- 1,223
- References
- 0
- FWCI
- 22.05
- Type
- journal article
- Language
- en
- Open access
- closed
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