# American Institute of Mathematical Sciences

April  2015, 11(2): 345-364. doi: 10.3934/jimo.2015.11.345

## A new auxiliary function method for systems of nonlinear equations

 1 School of Mathematics, Chongqing Normal University, Chongqing 401331, China, China, China 2 Department of Mathematics, Shanghai University, Shanghai 200444

Received  November 2013 Revised  May 2014 Published  September 2014

In this paper, we present a new global optimization method to solve nonlinear systems of equations. We reformulate given system of nonlinear equations as a global optimization problem and then give a new auxiliary function method to solve the reformulated global optimization problem. The new auxiliary function proposed in this paper can be a filled function, a quasi-filled function or a strict filled function with appropriately chosen parameters. Several numerical examples are presented to illustrate the efficiency of the present approach.
Citation: Zhiyou Wu, Fusheng Bai, Guoquan Li, Yongjian Yang. A new auxiliary function method for systems of nonlinear equations. Journal of Industrial & Management Optimization, 2015, 11 (2) : 345-364. doi: 10.3934/jimo.2015.11.345
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