An accelerated variant of the projection based parallel hybrid algorithm for split null point problems
DOI:
https://doi.org/10.12775/TMNA.2022.015Keywords
Parallel hybrid algorithm, inertial extrapolation, strong convergence, null point problemAbstract
In this paper, we consider an accelerated shrinking projection based parallel hybrid algorithm to study the split null point problem (SNPP) associated with the maximal monotone operators in Hilbert spaces. The analysis of the proposed algorithm provides strong convergence results under suitable set of control conditions as well as viability with the help of a numerical experiment. The results presented in this paper improve various existing results in the current literature.References
F. Alvarez and H. Attouch, An inertial proximal method for monotone operators via discretization of a nonlinear oscillator with damping, Set-Valued Anal. 9 (2001), 3–11.
Y. Arfat, O.S. Iyiola, M.A.A. Khan, P. Kumam, W. Kumam and K. Sitthithakerngkiet, Convergence analysis of the shrinking approximants for fixed point problem and generalized split common null point problem, J. Inequal. Appl. 67 (2022), 1–21.
Y. Arfat, M.A.A. Khan, P. Kumam, W. Kumam and K. Sitthithakerngkiet, Iterative solutions via some variants of extragradient approximants in Hilbert spaces, AIMS Math. 7 (2022), no. 8, 13910–13926.
Y. Arfat, P. Kumam, M.A.A. Khan, P.S. Ngiamsunthorn and A. Kaewkhao, An inertially constructed forward-backward splitting algorithm in Hilbert spaces, Adv. Difference Equ. 124 (2021).
Y. Arfat, P. Kumam, M.A.A. Khan, P.S. Ngiamsunthorn and A. Kaewkhao, A parallel hybrid accelerated extragradient algorithm for pseudomonotone equilibrium, fixed point, and split null point problems, Adv. Difference Equ. 364 (2021).
Y. Arfat, P. Kumam, M.A.A. Khan and P.S. Ngiamsunthorn, An accelerated projection based parallel hybrid algorithm for fixed point and split null point problems in Hilbert spaces, Math. Meth. Appl. Sci. (2021), 1–19.
Y. Arfat, P. Kumam, M.A.A. Khan and P.S. Ngiamsunthorn, Parallel shrinking inertial extragradient approximants for pseudomonotone equilibrium, fixed point and generalized split null point problem, Ricerche Mat. (2021), DOI: 10.1007/s11587-021-00647-4.
Y. Arfat, P. Kumam, M.A.A. Khan and P. S. Ngiamsunthorn, Shrinking approximants for fixed point problem and generalized split null point problem in Hilbert spaces, Optim. Lett. 16 (2022), 1895–1913.
Y. Arfat, P. Kumam, M.A.A. Khan and O. S. Iyiola, Multi-inertial parallel hybrid projection algorithm for generalized split null point problems, J. Appl. Math. Comput. (2021), DOI: 10.1007/s12190-021-01660-4.
H.H. Bauschke and P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces, CMS Books in Mathematics, Springer, New York, 2011.
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Probl. 20 (2004), no. 1, 103–120.
C. Byrne, Y. Censor, A. Gibali and S. Reich, The split common null point problem, J. Nonlinear Convex Anal. 13 (2012), 759–775.
Y. Censor and T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms 8 (1994), 221–239.
Y. Censor, T. Elfving, N. Kopf and T. Bortfeld, The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Probl. 21 (2005), 2071–2084.
Y. Censor, A. Gibali and S. Reich, Algorithms for the split variational inequality problem, Numer. Algorithms 59 (2012), 301–323.
Y. Censor and A. Segal, The split common fixed point problem for directed operators, J. Nonlinear Convex Anal. 16 (2009), 587–600.
P.L. Combettes, The convex feasibility problem in image recovery, Adv. Imaging Electron Phys. 95 (1996), 155–453.
V. Dadashi, Shrinking projection algorithms for the split common null point problem, Bull. Aust. Math. Soc. 99 (2017), 299–306.
A. Gibali, A new split inverse problem and an application to least intensity feasible solutions, Pure. Appl. Func. Anal. 2 (2017), 243–258.
D.V. Hieu, L.D. Muu and P.K. Anh, Parallel hybrid extragradient methods for pseudomonotone equilibrium problems and nonexpansive mappings, Numer. Algorithms 73 (2016), 197–217.
C. Martinez-Yanes and H.K. Xu, Strong convergence of CQ method for fixed point iteration processes, Nonlinear Anal, 64 (2006), 2400–2411.
J.J. Moreau, Prosimite et dualite dans un espace Hilbertien, Bull. Soc. Math. France 93 (1965), 273–299.
A. Moudafi and M. Oliny, Convergence of a splitting inertial proximal method for monotone operators, J. Comput. Appl. Math. 155 (2003), 447–454.
B.T. Polyak, Some methods of speeding up the convergence of iteration methods, U.S.S.R. Comput. Math. Math. Phys. 4 (1964), no. 5, 1–17.
R.T. Rockafellar, On the maximality of sums of nonlinear monotone operators, Trans. Amer. Math. Soc. 149 (1970), 75–88.
S. Reich and T.M. Tuyen, A new algorithm for solving the split common null point problem in Hilbert spaces, Numer. Algorithms 83 (2020), 789–805.
S. Takahashi and W. Takahashi, The split common null point problem and the shrinking projection method in Banach spaces, Optimization. 65 (2016), 281–287.
R. Tibshirani, Regression shrinkage and selection via lasso, J. R. Stat. Soc. Ser. B Stat. Methodol. 58 (1996), 267–288.
F. Wang, A new iterative method for the split common fixed point problem in Hilbert spaces, Optimization 66 (2017), 407–415.
H.K. Xu, Iterative methods for the split feasibility problem in infinite dimensional Hilbert spaces, Inverse Probl. 26 (2010), article ID 105018.
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Yasir Arfat, Poom Kumam, Muhammad Aqeel Ahmad Khan, Parinya Sa Ngiamsunthorn
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Stats
Number of views and downloads: 0
Number of citations: 0
