Strong convergence of a forward–backward splitting method with a new step size for solving monotone inclusions

2019 ◽  
Vol 38 (2) ◽  
Author(s):  
Duong Viet Thong ◽  
Prasit Cholamjiak
Keyword(s):  
Strong Convergence ◽  
Splitting Method ◽  
Step Size ◽  
Monotone Inclusions

scholarly journals Strong convergence of an inertial forward-backward splitting method for accretive operators in real Banach space

2020 ◽  
Vol 21 (2) ◽  
pp. 397-412 ◽  
Author(s):  
H.A. Abass ◽  
◽  
C. Izuchukwu ◽  
O.T. Mewomo ◽  
Q.L. Dong ◽  
...  
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Real Banach Space ◽  
Splitting Method ◽  
Accretive Operators

scholarly journals Relaxed Inertial Tseng’s Type Method for Solving the Inclusion Problem with Application to Image Restoration

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 818 ◽  
Author(s):  
Jamilu Abubakar ◽  
Poom Kumam ◽  
Abdulkarim Hassan Ibrahim ◽  
Anantachai Padcharoen
Keyword(s):  
Lipschitz Constant ◽  
Monotone Mapping ◽  
Splitting Method ◽  
Split Feasibility Problem ◽  
Monotone Operators ◽  
Feasibility Problem ◽  
Inclusion Problem ◽  
Variable Step Size ◽  
Step Size ◽  
Type Method

The relaxed inertial Tseng-type method for solving the inclusion problem involving a maximally monotone mapping and a monotone mapping is proposed in this article. The study modifies the Tseng forward-backward forward splitting method by using both the relaxation parameter, as well as the inertial extrapolation step. The proposed method follows from time explicit discretization of a dynamical system. A weak convergence of the iterates generated by the method involving monotone operators is given. Moreover, the iterative scheme uses a variable step size, which does not depend on the Lipschitz constant of the underlying operator given by a simple updating rule. Furthermore, the proposed algorithm is modified and used to derive a scheme for solving a split feasibility problem. The proposed schemes are used in solving the image deblurring problem to illustrate the applicability of the proposed methods in comparison with the existing state-of-the-art methods.

scholarly journals Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 156 ◽  
Author(s):  
Chanjuan Pan ◽  
Yuanheng Wang
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Minimization Problem ◽  
Numerical Experiments ◽  
Splitting Method ◽  
Splitting Methods ◽  
Strong Convergence Theorem ◽  
Accretive Operators ◽  
Convex Minimization Problem ◽  
Inertial Extrapolation

In this article, we study a modified viscosity splitting method combined with inertial extrapolation for accretive operators in Banach spaces and then establish a strong convergence theorem for such iterations under some suitable assumptions on the sequences of parameters. As an application, we extend our main results to solve the convex minimization problem. Moreover, the numerical experiments are presented to support the feasibility and efficiency of the proposed method.

scholarly journals A Parallel Splitting Method for Coupled Monotone Inclusions

2010 ◽  
Vol 48 (5) ◽  
pp. 3246-3270 ◽  
Author(s):  
Hédy Attouch ◽  
Luis M. Briceño-Arias ◽  
Patrick L. Combettes
Keyword(s):  
Splitting Method ◽  
Monotone Inclusions ◽  
Parallel Splitting

scholarly journals Iterative Design for the Common Solution of Monotone Inclusions and Variational Inequalities

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1504
Author(s):  
Li Wei ◽  
Xin-Wang Shen ◽  
Ravi P. Agarwal
Keyword(s):  
Hilbert Space ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Real Hilbert Space ◽  
Iterative Algorithms ◽  
Iterative Design ◽  
Common Solution ◽  
Monotone Inclusions ◽  
New Ideas ◽  
The Common

Some new forward–backward multi-choice iterative algorithms with superposition perturbations are presented in a real Hilbert space for approximating common solution of monotone inclusions and variational inequalities. Some new ideas of constructing iterative elements can be found and strong convergence theorems are proved under mild restrictions, which extend and complement some already existing work.

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