scholarly journals Finding Global Minima with a Filled Function Approach for Non-Smooth Global Optimization

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Weixiang Wang ◽  
Youlin Shang ◽  
Ying Zhang
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Numerical Test ◽  
Function Approach ◽  
Global Optimization Problem ◽  
Computational Results ◽  
Filled Function ◽  
Global Minima ◽  
Smooth Case ◽  
Definition Of

A filled function approach is proposed for solving a non-smooth unconstrained global optimization problem. First, the definition of filled function in Zhang (2009) for smooth global optimization is extended to non-smooth case and a new one is put forwarded. Then, a novel filled function is proposed for non-smooth the global optimization and a corresponding non-smooth algorithm based on the filled function is designed. At last, a numerical test is made. The computational results demonstrate that the proposed approach is effcient and reliable.

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.

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.

scholarly journals A Filled Function Approach for Nonsmooth Constrained Global Optimization

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Weixiang Wang ◽  
Youlin Shang ◽  
Ying Zhang
Keyword(s):  
Global Optimization ◽  
Constrained Optimization ◽  
Unconstrained Optimization ◽  
Penalty Function ◽  
Optimization Problem ◽  
Solution Algorithm ◽  
Constrained Global Optimization ◽  
Filled Function ◽  
Global Minima ◽  
Constrained Optimization Problem

A novel filled function is given in this paper to find a global minima for a nonsmooth constrained optimization problem. First, a modified concept of the filled function for nonsmooth constrained global optimization is introduced, and a filled function, which makes use of the idea of the filled function for unconstrained optimization and penalty function for constrained optimization, is proposed. Then, a solution algorithm based on the proposed filled function is developed. At last, some preliminary numerical results are reported. The results show that the proposed approach is promising.

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