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.

scholarly journals A Novel Filled Function Method for Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Liuyang Yuan ◽  
Qiuhua Tang
Keyword(s):  
Global Optimization ◽  
Nonlinear Equations ◽  
Function Method ◽  
Optimization Problem ◽  
Constrained Systems ◽  
Systems Of Nonlinear Equations ◽  
Test Problems ◽  
Global Optimization Problem ◽  
Filled Function ◽  
Filled Function Method

A novel filled function method is suggested for solving box-constrained systems of nonlinear equations. Firstly, the original problem is converted into an equivalent global optimization problem. Subsequently, a novel filled function with one parameter is proposed for solving the converted global optimization problem. Some properties of the filled function are studied and discussed. Finally, an algorithm based on the proposed novel filled function for solving systems of nonlinear equations is presented. The objective function value can be reduced by quarter in each iteration of our algorithm. The implementation of the algorithm on several test problems is reported with satisfactory numerical results.

A Generalized Filled Function for Non-Smooth Constrained Global Optimization

2011 ◽  
Vol 204-210 ◽  
pp. 114-117
Author(s):  
Wei Xiang Wang ◽  
You Lin Shang ◽  
Lian Sheng Zhang
Keyword(s):  
Global Optimization ◽  
Numerical Experiments ◽  
Function Method ◽  
Optimization Problem ◽  
Solution Algorithm ◽  
Global Optimization Problem ◽  
Computational Results ◽  
Constrained Global Optimization ◽  
Filled Function ◽  
Filled Function Method

A generalized filled function method is developed in this paper to solve nonsmooth constrained global optimization problem. Theoretical properties of the proposed function is investigated, and a solution algorithm is proposed. Numerical experiments are also reported in this paper. The preliminary computational results show that the proposed method is promising.

A new filled function method for nonlinear equations

2009 ◽  
Vol 210 (2) ◽  
pp. 411-421 ◽  
Author(s):  
Youjiang Lin ◽  
Yongjian Yang ◽  
M. Mammadov
Keyword(s):  
Nonlinear Equations ◽  
Function Method ◽  
Filled Function ◽  
Filled Function Method

A filled function method for nonlinear equations

2007 ◽  
Vol 189 (2) ◽  
pp. 1196-1204 ◽  
Author(s):  
Z.Y. Wu ◽  
M. Mammadov ◽  
F.S. Bai ◽  
Y.J. Yang
Keyword(s):  
Nonlinear Equations ◽  
Function Method ◽  
Filled Function ◽  
Filled Function Method
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