scholarly journals Strong Convergence of a New Iterative Algorithm for Split Monotone Variational Inclusion Problems

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 123 ◽  
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Iterative Method ◽  
Hilbert Spaces ◽  
Optimization Problem ◽  
Variational Inclusion ◽  
Hierarchical Optimization ◽  
Inclusion Problem ◽  
Inclusion Problems ◽  
Infinite Dimensional ◽  
Variational Inclusion Problem ◽  
General Iterative Method

The main aim of this work is to introduce an implicit general iterative method for approximating a solution of a split variational inclusion problem with a hierarchical optimization problem constraint for a countable family of mappings, which are nonexpansive, in the setting of infinite dimensional Hilbert spaces. Convergence theorem of the sequences generated in our proposed implicit algorithm is obtained under some weak assumptions.

scholarly journals Multi-Step Inertial Hybrid and Shrinking Tseng’s Algorithm with Meir–Keeler Contractions for Variational Inclusion Problems

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1548
Author(s):  
Yuanheng Wang ◽  
Mingyue Yuan ◽  
Bingnan Jiang
Keyword(s):  
Projection Method ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Inertial Method ◽  
Inclusion Problems ◽  
Variational Inclusion Problem ◽  
Convex Minimization Problems ◽  
Tseng’S Method

In our paper, we propose two new iterative algorithms with Meir–Keeler contractions that are based on Tseng’s method, the multi-step inertial method, the hybrid projection method, and the shrinking projection method to solve a monotone variational inclusion problem in Hilbert spaces. The strong convergence of the proposed iterative algorithms is proven. Using our results, we can solve convex minimization problems.

scholarly journals A modified proximal point algorithm for solving variational inclusion problem in real Hilbert spaces

2020 ◽  
Vol 2020 (1) ◽  
pp. 28-39
Author(s):  
Thierno M. M. Sow
Keyword(s):  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Proximal Point Algorithm ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Proximal Point ◽  
Inclusion Problems ◽  
Common Solution ◽  
Variational Inclusion Problem ◽  
The Common

AbstractThe purpose of this paper is to use a modified proximal point algorithm for solving variational inclusion problem in real Hilbert spaces. It is proven that the sequence generated by the proposed iterative algorithm converges strongly to the common solution of the convex minimization and variational inclusion problems.

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 Modified Proximal Algorithms for Finding Solutions of the Split Variational Inclusions

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 708 ◽  
Author(s):  
Suthep Suantai ◽  
Suparat Kesornprom ◽  
Prasit Cholamjiak
Keyword(s):  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Signal Recovery ◽  
Proximal Algorithms ◽  
Split Variational Inclusion Problem ◽  
Variational Inclusion Problem ◽  
Lipschitz Constants ◽  
Theoretical Results

We investigate the split variational inclusion problem in Hilbert spaces. We propose efficient algorithms in which, in each iteration, the stepsize is chosen self-adaptive, and proves weak and strong convergence theorems. We provide numerical experiments to validate the theoretical results for solving the split variational inclusion problem as well as the comparison to algorithms defined by Byrne et al. and Chuang, respectively. It is shown that the proposed algorithms outrun other algorithms via numerical experiments. As applications, we apply our method to compressed sensing in signal recovery. The proposed methods have as a main advantage that the computation of the Lipschitz constants for the gradient of functions is dropped in generating the sequences.

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