Converse Inertial Step Approach and Its Applications in Solving Nonexpansive Mapping
Year: 2025
Type: article
Abstract: In spite of great successes of the inertial step approach (ISA) in various fields, we are investigating the converse inertial step approach (CISA) for the first time. First, the classical Picard iteration for solving nonexpansive mappings converges weakly with CISA integration. Its analysis is based on the newly developed weak quasi-Fejér monotonicity under mild assumptions. We also establish O(1/kγ) (γ∈(0,1)) and linear convergence rate under different assumptions. This extends the O(1/k) convergence rate of the Krasnosel’skiĭ–Mann iteration. A generalized version of CISA is then studied. Second, combining CISA with over-relaxed step approach for solving nonexpansive mappings leads to a new algorithm, which not only converges without restrictive assumptions but also allows an inexact calculation in each iteration. Third, with CISA integration, a Backward–Forward splitting algorithm succeeds in accepting a larger step-size, and a Peaceman–Rachford splitting algorithm is guaranteed to converge.
Source: Mathematics
DOI: 10.3390/math13223722
Authors: Gangxing Yan, Tao Zhang
Institutions: City University of Macau, Linyi University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4416409582