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 inarXiv.org
Main Authors D Russell Luke, Malitsky, Yura
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.01.2018
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ISSN2331-8422
DOI10.48550/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.
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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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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SubjectTerms Algorithms
Convergence
Convexity
Mathematical analysis
Mathematics - Optimization and Control
Matrix methods
Numerical methods
Smoothness
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