{"ID":2864293,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.23817","arxiv_id":"2509.23817","title":"Weak and strong convergence of a relaxed inertial proximal splitting algorithm for solving hierarchical equilibrium problems","abstract":"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.","short_abstract":"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 c...","url_abs":"https://arxiv.org/abs/2509.23817","url_pdf":"https://arxiv.org/pdf/2509.23817v1","authors":"[\"Zakaria Mazgouri\",\"Hassan Riahi\",\"Michel Théra\"]","published":"2025-09-28T11:44:14Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}