scholarly journals Iterative approximation of solution of split variational inclusion problem

Filomat ◽  
2018 ◽  
Vol 32 (8) ◽  
pp. 2921-2932 ◽  
Author(s):  
Jeremiah Ezeora ◽  
Chinedu Izuchukwu
Keyword(s):  
Convex Optimization ◽  
Hilbert Spaces ◽  
Optimization Problems ◽  
Optimization Theory ◽  
Variational Problems ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Iterative Approximation ◽  
Convex Optimization Problems ◽  
Variational Inclusion Problem

Following recent important results of Moudafi [Journal of Optimization Theory and Applications 150(2011), 275-283] and other related results on variational problems, we introduce a new iterative algorithm for approximating a solution of monotone variational inclusion problem involving multi-valued mapping. The sequence of the algorithm is proved to converge strongly in the setting of Hilbert spaces. As application, we solved split convex optimization problems.

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.

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.

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