Projective splitting with backward, half-forward and proximal-Newton steps
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909191601389568 |
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| author | Alves, M. Marques |
| author_facet | Alves, M. Marques |
| contents | We propose and study the weak convergence of a projective splitting algorithm for solving multi-term composite monotone inclusion problems involving the finite sum of $n$ maximal monotone operators, each of which having an inner four-block structure: sum of maximal monotone, Lipschitz continuous, cocoercive and smooth differentiable operators. We show how to perform backward and half-forward steps with respect to the maximal monotone and Lipschitz$+$cocoercive components, respectively, while performing proximal-Newton steps with respect to smooth differentiable blocks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10680 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Projective splitting with backward, half-forward and proximal-Newton steps Alves, M. Marques Optimization and Control We propose and study the weak convergence of a projective splitting algorithm for solving multi-term composite monotone inclusion problems involving the finite sum of $n$ maximal monotone operators, each of which having an inner four-block structure: sum of maximal monotone, Lipschitz continuous, cocoercive and smooth differentiable operators. We show how to perform backward and half-forward steps with respect to the maximal monotone and Lipschitz$+$cocoercive components, respectively, while performing proximal-Newton steps with respect to smooth differentiable blocks. |
| title | Projective splitting with backward, half-forward and proximal-Newton steps |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2208.10680 |