scholarly journals Convergence of Some Iterative Algorithms for System of Generalized Set-Valued Variational Inequalities

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
M. Akram ◽  
Aysha Khan ◽  
M. Dilshad
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Existence Of A Solution ◽  
Banach Contraction ◽  
Parallel Iterative Algorithms ◽  
Parallel Iterative

In this article, we consider and study a system of generalized set-valued variational inequalities involving relaxed cocoercive mappings in Hilbert spaces. Using the projection method and Banach contraction principle, we prove the existence of a solution for the considered problem. Further, we propose an iterative algorithm and discuss its convergence. Moreover, we establish equivalence between the system of variational inequalities and altering points problem. Some parallel iterative algorithms are proposed, and the strong convergence of the sequences generated by these iterative algorithms is discussed. Finally, a numerical example is constructed to illustrate the convergence analysis of the proposed parallel iterative algorithms.

scholarly journals Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1189 ◽  
Author(s):  
Yonghong Yao ◽  
Mihai Postolache ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Solution

In this paper, we are interested in the pseudomonotone variational inequalities and fixed point problem of pseudocontractive operators in Hilbert spaces. An iterative algorithm has been constructed for finding a common solution of the pseudomonotone variational inequalities and fixed point of pseudocontractive operators. Strong convergence analysis of the proposed procedure is given. Several related corollaries are included.

scholarly journals A VLSI design concept for parallel iterative algorithms

2009 ◽  
Vol 7 ◽  
pp. 95-100 ◽  
Author(s):  
C. C. Sun ◽  
J. Götze
Keyword(s):  
Iterative Algorithm ◽  
Parallel Implementation ◽  
Vlsi Design ◽  
Iterative Algorithms ◽  
Point Of View ◽  
Design Strategies ◽  
Nano Technology ◽  
Present Design ◽  
Parallel Iterative Algorithms ◽  
Parallel Iterative

Abstract. Modern VLSI manufacturing technology has kept shrinking down to the nanoscale level with a very fast trend. Integration with the advanced nano-technology now makes it possible to realize advanced parallel iterative algorithms directly which was almost impossible 10 years ago. In this paper, we want to discuss the influences of evolving VLSI technologies for iterative algorithms and present design strategies from an algorithmic and architectural point of view. Implementing an iterative algorithm on a multiprocessor array, there is a trade-off between the performance/complexity of processors and the load/throughput of interconnects. This is due to the behavior of iterative algorithms. For example, we could simplify the parallel implementation of the iterative algorithm (i.e., processor elements of the multiprocessor array) in any way as long as the convergence is guaranteed. However, the modification of the algorithm (processors) usually increases the number of required iterations which also means that the switch activity of interconnects is increasing. As an example we show that a 25×25 full Jacobi EVD array could be realized into one single FPGA device with the simplified μ-rotation CORDIC architecture.

scholarly journals Iterative Solutions for Solving Variational Inequalities and Fixed-Point Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Li-Jun Zhu ◽  
Naseer Shahzad ◽  
Asim Asiri
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Fixed Point Problems ◽  
Suggested Algorithm ◽  
Iterative Solutions

In this paper, we are interested in variational inequalities and fixed-point problems in Hilbert spaces. We present an iterative algorithm for finding a solution of the studied variational inequalities and fixed-point problems. We show the strong convergence of the suggested algorithm.

scholarly journals Hybrid Iterations for the Fixed Point Problem and Variational Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Li-Jun Zhu ◽  
Shin Min Kang ◽  
Zhangsong Yao ◽  
Young Chel Kwun
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Iterative Algorithm ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Pseudocontractive Mappings

A hybrid iterative algorithm with Meir-Keeler contraction is presented for solving the fixed point problem of the pseudocontractive mappings and the variational inequalities. Strong convergence analysis is given aslimn→∞d(STxn,TSxn).

scholarly journals Analysis of Subgradient Extragradient Iterative Schemes for Variational Inequalities

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Danfeng Wu ◽  
Li-Jun Zhu ◽  
Zhuang Shan ◽  
Tzu-Chien Yin
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Convergence Analysis ◽  
Hilbert Spaces ◽  
Extragradient Method ◽  
Subgradient Extragradient Method ◽  
Iterative Schemes ◽  
Mild Conditions ◽  
Monotone Variational Inequality

In this paper, we investigate the monotone variational inequality in Hilbert spaces. Based on Censor’s subgradient extragradient method, we propose two modified subgradient extragradient algorithms with self-adaptive and inertial techniques for finding the solution of the monotone variational inequality in real Hilbert spaces. Strong convergence analysis of the proposed algorithms have been obtained under some mild conditions.

Iterative algorithm for the split equality problem in Hilbert spaces

2016 ◽  
Vol 22 (1) ◽  
Author(s):  
Godwin Chidi Ugwunnadi
Keyword(s):  
Strong Convergence ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Split Equality Problem ◽  
Equality Problem

AbstractIn this paper, we studied the split equality problems (SEP) with a new proposed iterative algorithm and established the strong convergence of the proposed algorithm to solution of the split equality problems (SEP).

scholarly journals An Iterative Algorithm for Solving Generalized Variational Inequalities and Fixed Points Problems

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 61 ◽  
Author(s):  
Yonghong Yao ◽  
Mihai Postolache ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Algorithm ◽  
Nonlinear Transformation ◽  
Generalized Variational Inequalities ◽  
Generalized Variational Inequality ◽  
Suggested Algorithm

In this paper, a generalized variational inequality and fixed points problem is presented. An iterative algorithm is introduced for finding a solution of the generalized variational inequalities and fixed point of two quasi-pseudocontractive operators under a nonlinear transformation. Strong convergence of the suggested algorithm is demonstrated.

Sign in / Sign up

Export Citation Format

Share Document