Vector direction of filled function method on solving unconstrained global optimization problem

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.

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A Generalized Filled Function for Non-Smooth Constrained Global Optimization

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.204-210.114 ◽

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.

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

Abstract and Applied Analysis ◽

10.1155/2011/209083 ◽

2011 ◽

Vol 2011 ◽

pp. 1-9 ◽

Cited By ~ 2

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.

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A new filled function method based on adaptive search direction and valley widening for global optimization

Applied Intelligence ◽

10.1007/s10489-020-02179-0 ◽

2021 ◽

Author(s):

Xiangjuan Wu ◽

Yuping Wang ◽

Ninglei Fan

Keyword(s):

Global Optimization ◽

Function Method ◽

Search Direction ◽

Adaptive Search ◽

Filled Function ◽

Filled Function Method

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

Discrete Dynamics in Nature and Society ◽

10.1155/2010/843609 ◽

2010 ◽

Vol 2010 ◽

pp. 1-10 ◽

Cited By ~ 1

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.

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