scholarly journals Stability analysis for generalized nonlinear mixed ordered implicit quasi-variational inclusion problem involving ⊕ operation

2022 ◽  
Keyword(s):  
Stability Analysis ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Variational Inclusion Problem

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 Generalized Implicit Set-Valued Variational Inclusion Problem with ⊕ Operation

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 421
Author(s):  
Rais Ahmad ◽  
Imran Ali ◽  
Saddam Husain ◽  
A. Latif ◽  
Ching-Feng Wen
Keyword(s):  
Resolvent Operator ◽  
Convergence Result ◽  
Variational Inclusion ◽  
Inclusion Problem ◽  
Variational Inclusion Problem ◽  
Special Cases ◽  
The Resolvent Operator

In this paper, we consider a resolvent operator which depends on the composition of two mappings with ⊕ operation. We prove some of the properties of the resolvent operator, that is, that it is single-valued as well as Lipschitz-type-continuous. An existence and convergence result is proven for a generalized implicit set-valued variational inclusion problem with ⊕ operation. Some special cases of a generalized implicit set-valued variational inclusion problem with ⊕ operation are discussed. An example is constructed to illustrate some of the concepts used in this paper.

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