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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 |
References:
[1] |
S. C. Billups and L. T. Watson, A probability-one homotopy algorithm for nonsmooth equations and mixed complementarity problems,, SIAM Journal on Optimization, 12 (2002), 606.
doi: 10.1137/S105262340037758X. |
[2] |
X. Chen, L. Qi and Y. F. Yang, Lagrangian globalization methods for nonlinear complementarity problem,, Journal of Optimization Theory and Applications, 112 (2002), 77.
doi: 10.1023/A:1013092412197. |
[3] |
B. Cetin, J. Barhen and J. Burdick, Terminal repeller unconstrained subenergy tunneling (TRUST) for fast global optimization,, J. Optim. Theory Appl., 77 (1993), 97.
doi: 10.1007/BF00940781. |
[4] |
A. R. Conn, N. I. M. Gould and P. L. Toint, Trust Region Methods,, SIAM, (2000).
doi: 10.1137/1.9780898719857. |
[5] |
J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations,, SIAM, (1996).
doi: 10.1137/1.9781611971200. |
[6] |
C. A. Floudas, P. M. Pardalos, C. S. Adjiman, W. R. Esposito, Z. H. Gumus, S. T. Harding, J. L. Klepeis, C. A. Meyer and C. A. Schweiger, Handbook of Test Problems in Local and Global Optimization,, Kluwer Academic Publishers, (1999).
doi: 10.1007/978-1-4757-3040-1. |
[7] |
R. Ge, A filled function method for finding a global minimizer of a function of several variables,, Mathematical Programming, 46 (1990), 191.
doi: 10.1007/BF01585737. |
[8] |
R. P. Ge and Y. Qin, A class of filled functions for finding global minimizers of a function of several variables,, Journal of Optimization Theory and Applications, 54 (1987), 241.
doi: 10.1007/BF00939433. |
[9] |
C. Kanzow, Global optimization techniques for mixed complementarity problems,, Journal of Global Optimization, 16 (2000), 1.
doi: 10.1023/A:1008331803982. |
[10] |
C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations,, SIAM, (1995).
doi: 10.1137/1.9781611970944. |
[11] |
J. Kostrowicki and L. Piela, Diffusion equation method of global minimization: Performance for standard test functions,, J. Optim. Theory Appl., 69 (1991), 269.
doi: 10.1007/BF00940643. |
[12] |
X. Liu, A computable filled function used for global optimization,, Appllied Mathematica and Computation, 126 (2002), 271.
doi: 10.1016/S0096-3003(00)00157-0. |
[13] |
X. Liu, A new filled function applied to global optimization,, Computers and Operations Research, 31 (2004), 61.
doi: 10.1016/S0305-0548(02)00154-5. |
[14] |
J. More, G. Burton and K. Hillstrom, User guide for MINPACK-1, Argonne National Labs Report ANL-80-74, Argonne, Illinois,, 1980., (). Google Scholar |
[15] |
J. L. Nazareth and L. Qi, Globalization of Newton's methods for solving nonlinear equations,, Numerical linear algebra with applications, 3 (1996), 239. Google Scholar |
[16] |
H. Sellami and S. M. Robinson, Implementation of a continuation method for normal maps,, Mathematical Programming, 76 (1997), 563.
doi: 10.1007/BF02614398. |
[17] |
X. J. Tong, L. Qi and Y. F. Yang, The Lagrangian globalization method for nonsmooth constrained equations,, Computational Optimization and Applications, 33 (2006), 89.
doi: 10.1007/s10589-005-5960-9. |
[18] |
Z. Y. Wu, M. Mammadov, F. S. Bai and Y. J. Yang, A filled function method for nonlinear equations,, Applied Mathematics and Computation, 189 (2007), 1196.
doi: 10.1016/j.amc.2006.11.183. |
[19] |
Z. Xu, H. X. Huang, P. M. Pardalos and C. X. Xu, Filled functions for unconstrained global optimization,, Journal of Global Optimization, 20 (2001), 49.
doi: 10.1023/A:1011207512894. |
[20] |
W. X. Zhu, Globally concavizied filled function method for the box constrained global minimization problem,, Optimization Methods and Software, 21 (2006), 653.
doi: 10.1080/10556780600628188. |
show all references
References:
[1] |
S. C. Billups and L. T. Watson, A probability-one homotopy algorithm for nonsmooth equations and mixed complementarity problems,, SIAM Journal on Optimization, 12 (2002), 606.
doi: 10.1137/S105262340037758X. |
[2] |
X. Chen, L. Qi and Y. F. Yang, Lagrangian globalization methods for nonlinear complementarity problem,, Journal of Optimization Theory and Applications, 112 (2002), 77.
doi: 10.1023/A:1013092412197. |
[3] |
B. Cetin, J. Barhen and J. Burdick, Terminal repeller unconstrained subenergy tunneling (TRUST) for fast global optimization,, J. Optim. Theory Appl., 77 (1993), 97.
doi: 10.1007/BF00940781. |
[4] |
A. R. Conn, N. I. M. Gould and P. L. Toint, Trust Region Methods,, SIAM, (2000).
doi: 10.1137/1.9780898719857. |
[5] |
J. E. Dennis and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations,, SIAM, (1996).
doi: 10.1137/1.9781611971200. |
[6] |
C. A. Floudas, P. M. Pardalos, C. S. Adjiman, W. R. Esposito, Z. H. Gumus, S. T. Harding, J. L. Klepeis, C. A. Meyer and C. A. Schweiger, Handbook of Test Problems in Local and Global Optimization,, Kluwer Academic Publishers, (1999).
doi: 10.1007/978-1-4757-3040-1. |
[7] |
R. Ge, A filled function method for finding a global minimizer of a function of several variables,, Mathematical Programming, 46 (1990), 191.
doi: 10.1007/BF01585737. |
[8] |
R. P. Ge and Y. Qin, A class of filled functions for finding global minimizers of a function of several variables,, Journal of Optimization Theory and Applications, 54 (1987), 241.
doi: 10.1007/BF00939433. |
[9] |
C. Kanzow, Global optimization techniques for mixed complementarity problems,, Journal of Global Optimization, 16 (2000), 1.
doi: 10.1023/A:1008331803982. |
[10] |
C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations,, SIAM, (1995).
doi: 10.1137/1.9781611970944. |
[11] |
J. Kostrowicki and L. Piela, Diffusion equation method of global minimization: Performance for standard test functions,, J. Optim. Theory Appl., 69 (1991), 269.
doi: 10.1007/BF00940643. |
[12] |
X. Liu, A computable filled function used for global optimization,, Appllied Mathematica and Computation, 126 (2002), 271.
doi: 10.1016/S0096-3003(00)00157-0. |
[13] |
X. Liu, A new filled function applied to global optimization,, Computers and Operations Research, 31 (2004), 61.
doi: 10.1016/S0305-0548(02)00154-5. |
[14] |
J. More, G. Burton and K. Hillstrom, User guide for MINPACK-1, Argonne National Labs Report ANL-80-74, Argonne, Illinois,, 1980., (). Google Scholar |
[15] |
J. L. Nazareth and L. Qi, Globalization of Newton's methods for solving nonlinear equations,, Numerical linear algebra with applications, 3 (1996), 239. Google Scholar |
[16] |
H. Sellami and S. M. Robinson, Implementation of a continuation method for normal maps,, Mathematical Programming, 76 (1997), 563.
doi: 10.1007/BF02614398. |
[17] |
X. J. Tong, L. Qi and Y. F. Yang, The Lagrangian globalization method for nonsmooth constrained equations,, Computational Optimization and Applications, 33 (2006), 89.
doi: 10.1007/s10589-005-5960-9. |
[18] |
Z. Y. Wu, M. Mammadov, F. S. Bai and Y. J. Yang, A filled function method for nonlinear equations,, Applied Mathematics and Computation, 189 (2007), 1196.
doi: 10.1016/j.amc.2006.11.183. |
[19] |
Z. Xu, H. X. Huang, P. M. Pardalos and C. X. Xu, Filled functions for unconstrained global optimization,, Journal of Global Optimization, 20 (2001), 49.
doi: 10.1023/A:1011207512894. |
[20] |
W. X. Zhu, Globally concavizied filled function method for the box constrained global minimization problem,, Optimization Methods and Software, 21 (2006), 653.
doi: 10.1080/10556780600628188. |
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