Global linear convergence in operator splitting methods
We establish necessary and sufficient conditions for linear convergence of operator splitting methods for a general class of convex optimization problems where the associated fixed-point operator is averaged. Most existing results establishing linear convergence in such methods require restrictive a...
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| Format: | Conference item |
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Institute of Electrical and Electronics Engineers
2016
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| _version_ | 1797084049784700928 |
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| author | Banjac, G Goulart, P |
| author_facet | Banjac, G Goulart, P |
| author_sort | Banjac, G |
| collection | OXFORD |
| description | We establish necessary and sufficient conditions for linear convergence of operator splitting methods for a general class of convex optimization problems where the associated fixed-point operator is averaged. Most existing results establishing linear convergence in such methods require restrictive assumptions regarding strong convexity and smoothness of the constituent functions in the optimization problem. However, there are several examples in the literature showing that linear convergence is possible even when these properties do not hold. We provide a unifying analysis method for establishing linear convergence based on linear regularity and show that many existing results are special cases of our approach. Moreover, we propose a novel linearly convergent splitting method for linear programming. |
| first_indexed | 2024-03-07T01:50:12Z |
| format | Conference item |
| id | oxford-uuid:99d60a52-3856-4b66-8b2d-c69314df27ce |
| institution | University of Oxford |
| last_indexed | 2024-03-07T01:50:12Z |
| publishDate | 2016 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | oxford-uuid:99d60a52-3856-4b66-8b2d-c69314df27ce2022-03-27T00:17:05ZGlobal linear convergence in operator splitting methodsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:99d60a52-3856-4b66-8b2d-c69314df27ceSymplectic Elements at OxfordInstitute of Electrical and Electronics Engineers2016Banjac, GGoulart, PWe establish necessary and sufficient conditions for linear convergence of operator splitting methods for a general class of convex optimization problems where the associated fixed-point operator is averaged. Most existing results establishing linear convergence in such methods require restrictive assumptions regarding strong convexity and smoothness of the constituent functions in the optimization problem. However, there are several examples in the literature showing that linear convergence is possible even when these properties do not hold. We provide a unifying analysis method for establishing linear convergence based on linear regularity and show that many existing results are special cases of our approach. Moreover, we propose a novel linearly convergent splitting method for linear programming. |
| spellingShingle | Banjac, G Goulart, P Global linear convergence in operator splitting methods |
| title | Global linear convergence in operator splitting methods |
| title_full | Global linear convergence in operator splitting methods |
| title_fullStr | Global linear convergence in operator splitting methods |
| title_full_unstemmed | Global linear convergence in operator splitting methods |
| title_short | Global linear convergence in operator splitting methods |
| title_sort | global linear convergence in operator splitting methods |
| work_keys_str_mv | AT banjacg globallinearconvergenceinoperatorsplittingmethods AT goulartp globallinearconvergenceinoperatorsplittingmethods |