2020/11/27 by Hui Ouyang, Ouyang, Hui
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Iterative Methods for Nonlinear Equations #Optimization and Variational Analysis #math.OC #msc:41A25 #msc:41A50 #msc:46B04 #msc:47H04 #msc:47H09 #msc:90C25
paper · pdf · doi:10.48550/arxiv.2011.13512
28 pages, 0 figure
arxiv created 2021/12/17 · arxiv updated 2021/12/20
In view of the great performance of circumcentered isometry methods for solving the best approximation problem, in this work we further investigate the locally proper circumcenter mapping and circumcentered method. Various examples of locally proper circumcenter mapping are presented and studied. Inspired by some results on circumcentered-reflection method by Behling, Bello-Cruz, and Santos in their recent papers, we provide sufficient conditions for one step convergence of circumcentered isometry methods for finding the best approximation point onto the intersection of fixed point sets of related isometries. In addition, we elaborate the performance of circumcentered reflection methods induced by reflectors associated with hyperplanes and halfspaces for finding the best approximation point onto (or a point in) the intersection of hyperplanes and halfspaces.