scholarly journals A Nonmonotone Projection Method for Constrained System of Nonlinear Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Yazheng Dang ◽  
Wenwen Liu
Keyword(s):  
Numerical Experiment ◽  
Nonlinear Equations ◽  
Suitable Condition ◽  
Projection Algorithm ◽  
Iterative Sequence ◽  
System Of Nonlinear Equations ◽  
Projection Algorithms ◽  
Constrained System ◽  
Slow Convergence ◽  
Constrained Nonlinear Equations

This paper deals with the nonmonotone projection algorithm for constrained nonlinear equations. For some starting points, the previous projection algorithms for the problem may encounter slow convergence which is related to the monotone behavior of the iterative sequence as well as the iterative direction. To circumvent this situation, we adopt the nonmonotone technique introduced by Dang to develop a nonmonotone projection algorithm. After constructing the nonmonotone projection algorithm, we show its convergence under some suitable condition. Preliminary numerical experiment is reported at the end of this paper, from which we can see that the algorithm we propose converges more quickly than that of the usual projection algorithm for some starting points.

scholarly journals An efficient gradient-free projection algorithm for constrained nonlinear equations and image restoration

2021 ◽  
Vol 6 (1) ◽  
pp. 235-260 ◽  
Author(s):  
Abdulkarim Hassan Ibrahim ◽  
◽  
Poom Kumam ◽  
Auwal Bala Abubakar ◽  
Umar Batsari Yusuf ◽  
...  
Keyword(s):  
Image Restoration ◽  
Nonlinear Equations ◽  
Projection Algorithm ◽  
Constrained Nonlinear Equations

scholarly journals New Double Projection Algorithm for Solving Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Lian Zheng
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Numerical Experiments ◽  
Variational Inequality Problem ◽  
Projection Algorithm ◽  
Iterative Sequence ◽  
Local Error ◽  
Projection Algorithms ◽  
Local Error Bound ◽  
Globally Convergent

We propose a class of new double projection algorithms for solving variational inequality problem, which can be viewed as a framework of the method of Solodov and Svaiter by adopting a class of new hyperplanes. By the separation property of hyperplane, our method is proved to be globally convergent under very mild assumptions. In addition, we propose a modified version of our algorithm that finds a solution of variational inequality which is also a fixed point of a given nonexpansive mapping. If, in addition, a certain local error bound holds, we analyze the convergence rate of the iterative sequence. Numerical experiments prove that our algorithms are efficient.

scholarly journals Finding the Roots of System of Nonlinear Equations by a Novel Filled Function Method

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Wei-Xiang Wang ◽  
You-Lin Shang ◽  
Wei-Gang Sun ◽  
Ying Zhang
Keyword(s):  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Function Method ◽  
Optimization Problem ◽  
Test Problems ◽  
System Of Nonlinear Equations ◽  
Global Optimization Problem ◽  
Filled Function ◽  
Filled Function Method ◽  
Constrained System

We present a novel filled function approach to solve box-constrained system of nonlinear equations. The system is first transformed into an equivalent nonsmooth global minimization problem, and then a new filled function method is proposed to solve this global optimization problem. Numerical experiments on several test problems are conducted and the computational results are also reported.

Solving System of Nonlinear Equations using Genetic Algorithm

2019 ◽  
Vol 10 (4) ◽  
pp. 877-886 ◽  
Author(s):  
Chhavi Mangla ◽  
Musheer Ahmad ◽  
Moin Uddin
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Equations ◽  
System Of Nonlinear Equations
Sign in / Sign up

Export Citation Format

Share Document