Wu, Zhiyou; Bai, Fusheng; Li, Guoquan; Yang, Yongjian A new auxiliary function method for systems of nonlinear equations. (English) Zbl 1304.90165 J. Ind. Manag. Optim. 11, No. 2, 345-364 (2015). Summary: 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. Cited in 1 Document MSC: 90C26 Nonconvex programming, global optimization Keywords:auxiliary function method; nonlinear equations; global optimization problems Software:minpack PDFBibTeX XMLCite \textit{Z. Wu} et al., J. Ind. Manag. Optim. 11, No. 2, 345--364 (2015; Zbl 1304.90165) Full Text: DOI References: [1] S. C. Billups, A probability-one homotopy algorithm for nonsmooth equations and mixed complementarity problems,, SIAM Journal on Optimization, 12, 606 (2002) · Zbl 1040.65043 [2] X. Chen, Lagrangian globalization methods for nonlinear complementarity problem,, Journal of Optimization Theory and Applications, 112, 77 (2002) · Zbl 1049.90098 [3] B. Cetin, Terminal repeller unconstrained subenergy tunneling (TRUST) for fast global optimization,, J. Optim. Theory Appl., 77, 97 (1993) · Zbl 0801.49001 [4] A. R. Conn, <em>Trust Region Methods</em>,, SIAM (2000) · Zbl 0958.65071 [5] J. E. Dennis, <em>Numerical Methods for Unconstrained Optimization and Nonlinear Equations</em>,, SIAM (1996) · Zbl 0847.65038 [6] C. A. Floudas, <em>Handbook of Test Problems in Local and Global Optimization</em>,, Kluwer Academic Publishers (1999) · Zbl 0943.90001 [7] R. Ge, A filled function method for finding a global minimizer of a function of several variables,, Mathematical Programming, 46, 191 (1990) · Zbl 0694.90083 [8] R. P. Ge, A class of filled functions for finding global minimizers of a function of several variables,, Journal of Optimization Theory and Applications, 54, 241 (1987) · Zbl 0595.65072 [9] C. Kanzow, Global optimization techniques for mixed complementarity problems,, Journal of Global Optimization, 16, 1 (2000) · Zbl 1009.90119 [10] C. T. Kelley, <em>Iterative Methods for Linear and Nonlinear Equations</em>,, SIAM (1995) · Zbl 0832.65046 [11] J. Kostrowicki, Diffusion equation method of global minimization: Performance for standard test functions,, J. Optim. Theory Appl., 69, 269 (1991) · Zbl 0725.65064 [12] X. Liu, A computable filled function used for global optimization,, Appllied Mathematica and Computation, 126, 271 (2002) · Zbl 1032.90027 [13] X. Liu, A new filled function applied to global optimization,, Computers and Operations Research, 31, 61 (2004) · Zbl 1039.90099 [14] J. More, User guide for MINPACK-1, Argonne National Labs Report ANL-80-74, Argonne, Illinois,, 1980. [15] J. L. Nazareth, Globalization of Newton’s methods for solving nonlinear equations,, Numerical linear algebra with applications, 3, 239 (1996) · Zbl 0858.65047 [16] H. Sellami, Implementation of a continuation method for normal maps,, Mathematical Programming, 76, 563 (1997) · Zbl 0873.90093 [17] X. J. Tong, The Lagrangian globalization method for nonsmooth constrained equations,, Computational Optimization and Applications, 33, 89 (2006) · Zbl 1103.90077 [18] Z. Y. Wu, A filled function method for nonlinear equations,, Applied Mathematics and Computation, 189, 1196 (2007) · Zbl 1122.65355 [19] Z. Xu, Filled functions for unconstrained global optimization,, Journal of Global Optimization, 20, 49 (2001) · Zbl 1049.90092 [20] W. X. Zhu, Globally concavizied filled function method for the box constrained global minimization problem,, Optimization Methods and Software, 21, 653 (2006) · Zbl 1113.90126 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.