scholarly journals The Penalty Method for a New System of Generalized Variational Inequalities

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
Yu-Chao Tang ◽  
Li-Wei Liu
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Penalty Method ◽  
Existence Of Solution ◽  
Penalty Methods ◽  
Generalized Variational Inequalities ◽  
New System

We consider a new system of generalized variational inequalities (SGVI). Using the penalty methods, we prove the existence of solution of SGVI in Hilbert spaces. Our results extend and improve some known results.

scholarly journals Convergence Analysis of ParallelS-Iteration Process for System of Generalized Variational Inequalities

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
D. R. Sahu ◽  
Shin Min Kang ◽  
Ajeet Kumar
Keyword(s):  
Hilbert Space ◽  
Variational Inequalities ◽  
Real Hilbert Space ◽  
Iteration Process ◽  
Mann Iteration ◽  
Generalized Variational Inequalities ◽  
Parallel Iteration ◽  
Mann Iteration Process ◽  
Iteration Processes ◽  
New System

We consider a new system of generalized variational inequalities (SGVI) defined on two closed convex subsets of a real Hilbert space. To find the solution of considered SGVI, a parallel Mann iteration process and a parallelS-iteration process have been proposed and the strong convergence of the sequences generated by these parallel iteration processes is discussed. Numerical example illustrates that the proposed parallelS-iteration process has an advantage over parallel Mann iteration process in computing altering points of some mappings.

scholarly journals Algorithm for Solving a New System of Generalized Variational Inclusions in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Shamshad Husain ◽  
Sanjeev Gupta
Keyword(s):  
Variational Inequalities ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Existence Of Solutions ◽  
Variational Inclusions ◽  
Special Cases ◽  
Systems Of Variational Inequalities ◽  
Cocoercive Operators ◽  
New System

We introduce and study a new system of generalized variational inclusions involving -cocoercive and relaxed -cocoercive operators, which contain the systems of variational inclusions and the systems of variational inequalities, variational inclusions, and variational inequalities as special cases. By using the resolvent technique for the -cocoercive operators, we prove the existence of solutions and the convergence of a new iterative algorithm for this system of variational inclusions in Hilbert spaces. An example is given to justify the main result. Our results can be viewed as a generalization of some known results in the literature.

scholarly journals An Efficient Parallel Extragradient Method for Systems of Variational Inequalities Involving Fixed Points of Demicontractive Mappings

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1915
Author(s):  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Line Search ◽  
Convex Combination ◽  
Extragradient Method ◽  
Convergence Result ◽  
Armijo Line Search ◽  
Systems Of Variational Inequalities ◽  
Demicontractive Mappings ◽  
The Cost

Herein, we present a new parallel extragradient method for solving systems of variational inequalities and common fixed point problems for demicontractive mappings in real Hilbert spaces. The algorithm determines the next iterate by computing a computationally inexpensive projection onto a sub-level set which is constructed using a convex combination of finite functions and an Armijo line-search procedure. A strong convergence result is proved without the need for the assumption of Lipschitz continuity on the cost operators of the variational inequalities. Finally, some numerical experiments are performed to illustrate the performance of the proposed method.

Penalty methods for a system of constrained variational inequalities

2010 ◽  
Vol 6 (3) ◽  
pp. 451-458 ◽  
Author(s):  
Abdellatif Moudafi ◽  
Muhammad Aslam Noor
Keyword(s):  
Variational Inequalities ◽  
Penalty Methods
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