Weak and strong convergence of a relaxed inertial proximal splitting algorithm for solving hierarchical equilibrium problems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912612843782144 |
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| author | Mazgouri, Zakaria Riahi, Hassan Théra, Michel |
| author_facet | Mazgouri, Zakaria Riahi, Hassan Théra, Michel |
| contents | In this chapter, we introduce the relaxed inertial proximal splitting algorithm (RIPSA) for hierarchical equilibrium problems. Using Opial-Passty's lemma, we first establish weak ergodic and weak convergence of the sequence generated by the algorithm to a solution of the problem, in the absence of the Browder-Halpern contraction factor. We then derive a strong convergence result under an additional strong monotonicity assumption. Subsequently, we relax this requirement by removing strong monotonicity and instead incorporating a Browder-Halpern contraction factor into (RIPSA), which guarantees strong convergence to a solution determined by the contraction factor. Finally, we discuss two related settings: convex minimization problems and monotone variational inequalities formulated as fixed-point problems for nonexpansive operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Weak and strong convergence of a relaxed inertial proximal splitting algorithm for solving hierarchical equilibrium problems Mazgouri, Zakaria Riahi, Hassan Théra, Michel Optimization and Control In this chapter, we introduce the relaxed inertial proximal splitting algorithm (RIPSA) for hierarchical equilibrium problems. Using Opial-Passty's lemma, we first establish weak ergodic and weak convergence of the sequence generated by the algorithm to a solution of the problem, in the absence of the Browder-Halpern contraction factor. We then derive a strong convergence result under an additional strong monotonicity assumption. Subsequently, we relax this requirement by removing strong monotonicity and instead incorporating a Browder-Halpern contraction factor into (RIPSA), which guarantees strong convergence to a solution determined by the contraction factor. Finally, we discuss two related settings: convex minimization problems and monotone variational inequalities formulated as fixed-point problems for nonexpansive operators. |
| title | Weak and strong convergence of a relaxed inertial proximal splitting algorithm for solving hierarchical equilibrium problems |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2509.23817 |