scholarly journals General Split Variational Inclusion Problem in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li Yang ◽  
Fu Hai Zhao
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Split Variational Inclusion Problem ◽  
Variational Inclusion Problem

We consider a general split variational inclusion problem (GSFVIP) and propose an algorithm for finding the solutions of GSFVIP in Hilbert space. We establish the strong convergence of the proposed algorithm to a solution of GSFVIP. Our results extend and improve the related results in the literature.

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 An efficient iterative method for solving split variational inclusion problem with applications

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jamilu Abubakar ◽  
Poom Kumam ◽  
Abor Isa Garba ◽  
Muhammad Sirajo Abdullahi ◽  
Abdulkarim Hassan Ibrahim ◽  
...  
Keyword(s):  
Iterative Method ◽  
Strong Convergence ◽  
Iterative Scheme ◽  
Variational Inclusion ◽  
Strong Convergence Theorem ◽  
Inclusion Problem ◽  
Monotone Mappings ◽  
Bounded Linear ◽  
Split Variational Inclusion Problem ◽  
Variational Inclusion Problem

<p style='text-indent:20px;'>A new strong convergence iterative method for solving a split variational inclusion problem involving a bounded linear operator and two maximally monotone mappings is proposed in this article. The study considers an iterative scheme comprised of inertial extrapolation step together with the Mann-type step. A strong convergence theorem of the iterates generated by the proposed iterative scheme is given under suitable conditions. In addition, methods for solving variational inequality problems and split convex feasibility problems are derived from the proposed method. Applications of solving Nash-equilibrium problems and image restoration problems are solved using the derived methods to demonstrate the implementation of the proposed methods. Numerical comparisons with some existing iterative methods are also presented.</p>

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.

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