2025/09/28 by Zakaria Mazgouri, Mazgouri, Zakaria, Hassan Riahi +3
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.2509.23817
openalex publication_date 2025/09/28 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
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.