Graph splitting methods: Fixed points and strong convergence for linear subspaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908877312753664 |
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| author | Aragón-Artacho, Francisco J. Bauschke, Heinz H. Campoy, Rubén López-Pastor, César |
| author_facet | Aragón-Artacho, Francisco J. Bauschke, Heinz H. Campoy, Rubén López-Pastor, César |
| contents | In this paper, we develop a general analysis for the fixed points of the operators defining the graph splitting methods from [SIAM J. Optim., 34 (2024), pp. 1569-1594] by Bredies, Chenchene and Naldi. We particularize it to the case where the maximally monotone operators are normal cones of closed linear subspaces and provide an explicit formula for the limit points of the graph splitting schemes. We exemplify these results on some particular algorithms, unifying in this way some results previously derived as well as obtaining new ones. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_16564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graph splitting methods: Fixed points and strong convergence for linear subspaces Aragón-Artacho, Francisco J. Bauschke, Heinz H. Campoy, Rubén López-Pastor, César Optimization and Control 47H05, 47H09, 47N10, 65K05, 90C25 In this paper, we develop a general analysis for the fixed points of the operators defining the graph splitting methods from [SIAM J. Optim., 34 (2024), pp. 1569-1594] by Bredies, Chenchene and Naldi. We particularize it to the case where the maximally monotone operators are normal cones of closed linear subspaces and provide an explicit formula for the limit points of the graph splitting schemes. We exemplify these results on some particular algorithms, unifying in this way some results previously derived as well as obtaining new ones. |
| title | Graph splitting methods: Fixed points and strong convergence for linear subspaces |
| topic | Optimization and Control 47H05, 47H09, 47N10, 65K05, 90C25 |
| url | https://arxiv.org/abs/2505.16564 |