Convergence Analysis of Optimization Algorithms for Monotone Inclusion Problems

• Grant number: 23/04164-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2024
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Gabriel Haeser
• Grantee: Yasir Arfat
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 18/24293-0 - Computational methods in optimization, AP.TEM

Abstract

Recently, the Euclidean circumcenter technique has been employed in order to introduce circumcentered-reflection methods (CRM) for solving convex feasibility problems (CFP). The cir-cumcenter technique is simple yet an effective way of accelerating usual optimization algorithms.Since then, circumcenter-oriented optimization algorithms have been thoroughly analyzed in the setting of Euclidean spaces. On the other hand, Behling et al. [12] introduced a so-called cen-tralization of the CRM in Euclidean spaces in order to prove its convergence (see also [13]). This variant does not employ a product space reformulation for finding a point in the intersection of two closed convex sets. However, the extension of such results to the Hilbert space setting is only preliminary in the sense that only sets containing finitely many points were consideredin [8]. Inspired and motivated by these recent developments, we aim to develop further the circumcentered-oriented algorithms in Euclidean spaces together with providing a rigorous exten-sion of these methods, as well as its centralized variants, to the Hilbert space setting, considering both CFP and fixed point problems.