Filled function method for nonlinear equations

Authors:
Youjiang Lin;Yongjian Yang
Affiliations:
Department of Mathematics, Shanghai University, Shanghai 200444, PR China;Department of Mathematics, Shanghai University, Shanghai 200444, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 5
Cited 0

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Filled functions for unconstrained global optimization

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Abstract

Systems of nonlinear equations are ubiquitous in engineering, physics and mechanics, and have myriad applications. Generally, they are very difficult to solve. In this paper, we will present a filled function method to solve nonlinear systems. We will first convert the nonlinear systems into equivalent global optimization problems with the property: x^* is a global minimizer if and only if its function value is zero. A filled function method is proposed to solve the converted global optimization problem. Numerical examples are presented to illustrate our new techniques.