Convergence rate of the averaged CQ algorithms under Hölderian type bounded linear regularity property
Optimization Eruditorum, Volume 2, Issue 2, August 2025, Pages 146–156
CARISA KWOK WAI YU
Department of Mathematics, Statistics and Insurance, The Hang Seng University of Hong Kong, Shatin, Hong Kong, P. R. China
JINHUA WANG
School of Mathematical Sciences, Hangzhou Normal University, Hangzhou 311121, P. R. China
YIN LI
School of Mathematical Sciences, Shenzhen University, Shenzhen 518060, P. R. China
WEI ZHOU
School of Mathematical Sciences, Hangzhou Normal University, Hangzhou 311121, P. R. China
Abstract
We study the issue of the strong convergence together with estimates of convergence order of an averaged CQ algorithm for solving the split feasibility problem in Hilbert space. For this purpose, a Hölderian type bounded linear regularity property is introduced. When the involved parameters and stepsizes satisfy certain mild conditions, the strong convergence together with estimates of convergence order of the averaged CQ algorithm is established under the Hölderian type bounded linear regularity property. For the case when the involved parameters are all equal to constant 1, the averaged CQ algorithm is reduced to the well-known CQ algorithm. As applications, we obtain the strong convergence together with estimates of convergence order of the CQ algorithm, which extends the corresponding ones in (Wang, et al. Inverse Problem, 2017, 33: 055017). Finally, numerical experiments are presented to illustrate the effectiveness of the algorithm. Compared to other known algorithms, our algorithm performs better.
Cite this Article as
Carisa Kwok Wai Yu, Jinhua Wang, Yin Li, Wei Zhou, Convergence rate of the averaged CQ algorithms under Hölderian type bounded linear regularity property, Optimization Eruditorum, 2(2), 146–156, 2025