Iterative methods for fixed points and zero points of nonlinear mappings with applications. (3rd April 2021)

• Record Type: Journal Article
• Authors: Liu, Liya; Qin, Xiaolong; Agarwal, Ravi P.
• Is Part Of: Optimization. Volume 70:Number 4(2021)
• Page Start: 693
• Page End: 713
• Publication Date: 2021-04-03
• Subjects: Steepest-descent method -- nonexpansive mapping -- pseudomonotone mapping -- fixed point -- variational inequality; 47H05 -- 47H09 -- 49J40; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1613404
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The purpose of this article is to investigate a descent-type iterative algorithm for finding a common element of fixed-point sets of a finite family of nonexpansive mappings and zero-point sets of pseudomonotone mappings in Hilbert spaces. With suitable assumptions, we derive necessary and sufficient conditions for the strong convergence of the algorithm. Numerical examples and applications to signal processing problems are provided to support the main results.