TWO NEW INERTIAL RELAXED GRADIENT CQ ALGORITHMS ON THE SPLIT EQUALITY PROBLEM

Yuanheng Wang; Xueting Li; Bingnan Jiang

doi:10.11948/20210351

2022 Volume 12 Issue 1

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2022 > 12(1): 436-454

Next Article Previous Article

Yuanheng Wang, Xueting Li, Bingnan Jiang. TWO NEW INERTIAL RELAXED GRADIENT CQ ALGORITHMS ON THE SPLIT EQUALITY PROBLEM[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 436-454. doi: 10.11948/20210351

Citation:

Yuanheng Wang, Xueting Li, Bingnan Jiang. TWO NEW INERTIAL RELAXED GRADIENT CQ ALGORITHMS ON THE SPLIT EQUALITY PROBLEM[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 436-454. doi: 10.11948/20210351

TWO NEW INERTIAL RELAXED GRADIENT CQ ALGORITHMS ON THE SPLIT EQUALITY PROBLEM

1.
Department of Mathematics, Zhejiang Normal University, Jinhua 321000, China

Corresponding author: Email address: yhwang@zjnu.cn(Y. Wang)
Fund Project: The authors were supported by the National Natural Science Foundation of China (No. 12171435)

Abstract

Abstract

In order to better solve the split equality problems in Hilbert spaces, we propose two new algorithms. Combining inertial iteration methods, we construct an inertial simultaneous relaxed gradient CQ algorithm with adaptive step size, and prove its weak convergence under simpler and more straightforward conditions. Combining viscous iteration in the above algorithm, we construct an inertial viscosity simultaneous relaxed gradient CQ algorithm, and prove the strong convergence of the algorithm under simpler and more straightforward conditions. We also give some numerical experiments to compare with some known algorithms, which demonstrate the rationality and superiority of our algorithms in several rates of convergence.
- Split equality problem /
- inertial relaxed gradient CQ algorithm /
- viscosity algorithm /
- weak and strong convergence /
- split equality problem
MSC: 47H09, 47H10, 47H04

FullText(HTML)

References

[1]	C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstraction, Inverse Probl., 2004, 20(1), 103-120. doi: 10.1088/0266-5611/20/1/006 CrossRef Google Scholar
[2]	L. Ceng, Q. H. Ansari and J. Yao, Some iterative methods for finding fixed points and for solving constrained convex minimization problems, Nonlinear Anal., 2011, 74(16), 5286-5302. doi: 10.1016/j.na.2011.05.005 CrossRef Google Scholar
[3]	Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algor., 1994, 8(2), 221-239. doi: 10.1007/BF02142692 CrossRef Google Scholar
[4]	P. Cholamjiak, S. Suantai and P. Sunthrayuth, Stong convergence of a general viscosity explicit rule for the sum of two monotone operators in Hilbert spaces, J. Appl. Anal. Comput., 2019, 9(6), 2137-2155. Google Scholar
[5]	J. Fan, L. Liu and X. Qin, A subgradient extragradient algorithm with inertial effects for solving strongly pseudomonotone variational inequalities, Optimization, 2020, 69(9), 2199-2215. doi: 10.1080/02331934.2019.1625355 CrossRef Google Scholar
[6]	B. Jiang, Y. Wang and J. Yao, Multi-step inertial regularized methods for hierarchical variational inequality problems involving generalized Lipschitzian mappings, Mathematics, 2021, 9(17), Article ID 2103. Google Scholar
[7]	K. R. Kazmi, R. Ali and M. Furkan, Common solution to a split equality monotone variational inclusion problem, a split equality generalized general variational-like inequality problem and a split equality fixed point problem, Fixed Point Theory, 2019, 20(1), 211-231. doi: 10.24193/fpt-ro.2019.1.14 CrossRef Google Scholar
[8]	S. Kesornporm, N. Pholasa and P. Cholamjiak, On the convergenece analysis of the gradient-CQ algorithms for the split feasibility problem, Numner. Algor., 2020, 84(3), 997-1017. doi: 10.1007/s11075-019-00790-y CrossRef Google Scholar
[9]	L Lin and W. Takahashi, A general iterative method for hierarchical variational inequality problems in Hilbert spaces and applications, Positivity, 2012, 16(3), 429-453. doi: 10.1007/s11117-012-0161-0 CrossRef Google Scholar
[10]	R. Meštrović and D. Kalaj, A converse of Minkowski's type inequalities, J. Inequal. Appl., 2010, 2010, Article ID 461215. Google Scholar
[11]	A. Moudafi, A relaxed alternating CQ-algorithm for convex feasibility problems, Nonlinear Anal., 2013, 79, 117-121. doi: 10.1016/j.na.2012.11.013 CrossRef Google Scholar
[12]	E. U. Ofoedu and N. N. Araka, Simultaneous approximation methods for common solution of equilibrium, fixed point and split equality problems, J. Nonlinear Convex Anal., 2019, 20(1), 85-101. Google Scholar
[13]	C. Pan and Y. Wang, Convergence theorems for modified inertial viscosity splitting methods in Banach spaces, Mathematics, 2019, 7(2), Article ID 156. Google Scholar
[14]	L. Shi, R. Chen and Y. Wu, Strong convergence of iterative algorithms for the split equality problem, J. Inequal. Appl., 2014, 2014, Article ID 478. Google Scholar
[15]	R. Shukla and R. Pant, Approximating solution of split equality and equilibrium problems by viscosity approximation algorithms, Comput. Appl. Math., 2018, 37(4), 5293-5314. doi: 10.1007/s40314-018-0637-z CrossRef Google Scholar
[16]	B. Tan, Z. Zhou and X. Qin, Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems, J. Appl. Anal. Comput., 2020, 10(5), 2184-2197. Google Scholar
[17]	D. Tian and L. Jiang, Two-step methods and relaxed two-step methods for solving the split equality problem, Comput. Appl. Math., 2021, 40(3), Article ID 83. Google Scholar
[18]	Y. Wang, C. Li and L. Lu, A new algorithm for the common solutions of a generalized variational inequality system and a nonlinear operator equation in Banach spaces, Mathematics, 2020, 8(11), Article ID 1944. Google Scholar
[19]	Y. Wang and C. Pan, Viscosity approximation methods for a general variational inequality system and fixed point problems in Banach spaces, Symmetry, 2020, 12(1), Article ID 36. Google Scholar
[20]	H. Xu, Iterative methods for the split feasibility problem in infinite-dimensional Hilbert space, Inverse Probl., 2010, 26(10), Article ID 105018. Google Scholar