Open AccessSteepest-descent block-iterative methods for a finite family of quasi-nonexpansive mappings
Author(s) -
Nguyễn Bường
Publication year - 2022
Publication title -
journal of industrial and management optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.325
H-Index - 32
eISSN - 1553-166X
pISSN - 1547-5816
DOI - 10.3934/jimo.2021133
Subject(s) - variational inequality , mathematics , fixed point , hilbert space , block (permutation group theory) , convergence (economics) , regular polygon , iterative method , discrete mathematics , mathematical optimization , combinatorics , pure mathematics , mathematical analysis , geometry , economics , economic growth
In this paper, for solving the variational inequality problem over the set of common fixed points of a finite family of demiclosed quasi-nonexpansive mappings in Hilbert spaces, we propose two new strongly convergent methods, constructed by specific combinations between the steepest-descent method and the block-iterative ones. The strong convergence is proved without the boundedly regular assumptions on the family of fixed point sets as well as the approximately shrinking property for each mapping of the family, that are usually assumed in recent literature for similar problems. Applications to the multiple-operator split common fixed point problem (MOSCFPP) and the problem of common minimum points of a finite family of lower semi-continuous convex functions with numerical experiments are given.