Monotonicity of Pairs of Operators and Generalized Inertial Proximal Method
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909994457235456 |
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| author | Le, Ba Khiet Mazgouri, Zakaria Théra, Michel |
| author_facet | Le, Ba Khiet Mazgouri, Zakaria Théra, Michel |
| contents | Monotonicity of pairs of operators is an extension of monotonicity of operators, which plays an important role in solving non-monotone inclusions. One of challenging problems in this new tool is how to design the associated mappings to obtain the monotone pairs. In this paper, we solve this problem and propose a Generalized Inertial Proximal Point Algorithm (GIPPA) using warped resolvents under the monotonicity of pairs. The weak, strong and linear convergence of the algorithm under some mild assumptions are established. We also provide numerical examples illustrating the implementability and effectiveness of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12738 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Monotonicity of Pairs of Operators and Generalized Inertial Proximal Method Le, Ba Khiet Mazgouri, Zakaria Théra, Michel Optimization and Control Monotonicity of pairs of operators is an extension of monotonicity of operators, which plays an important role in solving non-monotone inclusions. One of challenging problems in this new tool is how to design the associated mappings to obtain the monotone pairs. In this paper, we solve this problem and propose a Generalized Inertial Proximal Point Algorithm (GIPPA) using warped resolvents under the monotonicity of pairs. The weak, strong and linear convergence of the algorithm under some mild assumptions are established. We also provide numerical examples illustrating the implementability and effectiveness of the proposed method. |
| title | Monotonicity of Pairs of Operators and Generalized Inertial Proximal Method |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.12738 |