Block-coordinate primal-dual method for the nonsmooth minimization over linear constraints
We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence of the method without resorting to assumptions like smoothnes...
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| Published in | arXiv.org |
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| Main Authors | , |
| Format | Paper Journal Article |
| Language | English |
| Published |
Ithaca
Cornell University Library, arXiv.org
15.01.2018
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| Online Access | Get full text |
| ISSN | 2331-8422 |
| DOI | 10.48550/arxiv.1801.04782 |
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| Abstract | We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence of the method without resorting to assumptions like smoothness or strong convexity of the objective, full-rank condition on the matrix, strong duality or even consistency of the linear system. Freedom from imposing the latter assumption permits convergence guarantees for misspecified or noisy systems. |
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| AbstractList | Distributed and Large-Scale Optimization (2018) We consider the problem of minimizing a convex, separable, nonsmooth function
subject to linear constraints. The numerical method we propose is a
block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We
prove convergence of the method without resorting to assumptions like
smoothness or strong convexity of the objective, full-rank condition on the
matrix, strong duality or even consistency of the linear system. Freedom from
imposing the latter assumption permits convergence guarantees for misspecified
or noisy systems. We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a block-coordinate extension of the Chambolle-Pock primal-dual algorithm. We prove convergence of the method without resorting to assumptions like smoothness or strong convexity of the objective, full-rank condition on the matrix, strong duality or even consistency of the linear system. Freedom from imposing the latter assumption permits convergence guarantees for misspecified or noisy systems. |
| Author | D Russell Luke Malitsky, Yura |
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| BackLink | https://doi.org/10.1007/978-3-319-97478-1_6$$DView published paper (Access to full text may be restricted) https://doi.org/10.48550/arXiv.1801.04782$$DView paper in arXiv |
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| Copyright | 2018. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
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| DOI | 10.48550/arxiv.1801.04782 |
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| Snippet | We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints. The numerical method we propose is a... Distributed and Large-Scale Optimization (2018) We consider the problem of minimizing a convex, separable, nonsmooth function subject to linear constraints.... |
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| Title | Block-coordinate primal-dual method for the nonsmooth minimization over linear constraints |
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