Strong Convergence of Self-adaptive Inertial Algorithms for Solving Split Variational Inclusion Problems with Applications

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Bing Tan ◽  
Xiaolong Qin ◽  
Jen-Chih Yao
Keyword(s):  
Strong Convergence ◽  
Variational Inclusion ◽  
Inclusion Problems ◽  
Self Adaptive

scholarly journals Common Solution for a Finite Family of Equilibrium Problems, Quasi-Variational Inclusion Problems and Fixed Points on Hadamard Manifolds

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1161
Author(s):  
Jinhua Zhu ◽  
Jinfang Tang ◽  
Shih-sen Chang ◽  
Min Liu ◽  
Liangcai Zhao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Fixed Point Problem ◽  
Finite Family ◽  
Variational Inclusion ◽  
Point Problem ◽  
Hadamard Manifolds ◽  
Inclusion Problems ◽  
Common Solution

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

scholarly journals Two self-adaptive inertial projection algorithms for solving split variational inclusion problems

2021 ◽  
Vol 7 (4) ◽  
pp. 4960-4973
Author(s):  
Zheng Zhou ◽  
◽  
Bing Tan ◽  
Songxiao Li
Keyword(s):  
Hilbert Spaces ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Projection Algorithms ◽  
Approximation Solution ◽  
Inclusion Problems ◽  
Variational Inclusion Problem ◽  
Adaptive Stepsize ◽  
The Given ◽  
Self Adaptive

<abstract><p>This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of Hilbert spaces. For this purpose, inertial hybrid and shrinking projection algorithms are proposed under the effect of a self-adaptive stepsize which does not require information of the norms of the given operators. The strong convergence properties of the proposed algorithms are obtained under mild constraints. Finally, a numerical experiment is given to illustrate the performance of proposed methods and to compare our algorithms with an existing algorithm.</p></abstract>

scholarly journals Inducing strong convergence of trajectories in dynamical systems associated to monotone inclusions with composite structure

2020 ◽  
Vol 10 (1) ◽  
pp. 450-476
Author(s):  
Radu Ioan Boţ ◽  
Sorin-Mihai Grad ◽  
Dennis Meier ◽  
Mathias Staudigl
Keyword(s):  
Dynamical Systems ◽  
Strong Convergence ◽  
Equilibrium Problems ◽  
Monotone Operators ◽  
Inclusion Problem ◽  
Minimum Norm ◽  
Monotone Inclusion ◽  
Inclusion Problems ◽  
Monotone Inclusion Problem ◽  
Maximally Monotone Operators

Abstract In this work we investigate dynamical systems designed to approach the solution sets of inclusion problems involving the sum of two maximally monotone operators. Our aim is to design methods which guarantee strong convergence of trajectories towards the minimum norm solution of the underlying monotone inclusion problem. To that end, we investigate in detail the asymptotic behavior of dynamical systems perturbed by a Tikhonov regularization where either the maximally monotone operators themselves, or the vector field of the dynamical system is regularized. In both cases we prove strong convergence of the trajectories towards minimum norm solutions to an underlying monotone inclusion problem, and we illustrate numerically qualitative differences between these two complementary regularization strategies. The so-constructed dynamical systems are either of Krasnoselskiĭ-Mann, of forward-backward type or of forward-backward-forward type, and with the help of injected regularization we demonstrate seminal results on the strong convergence of Hilbert space valued evolutions designed to solve monotone inclusion and equilibrium problems.

Sign in / Sign up

Export Citation Format

Share Document