Particle swarm algorithm for solving systems of nonlinear equations

Solving systems of nonlinear equations is one of the most difficult problems in all of numerical computation and in a diverse range of engineering applications. Newton's method for solving systems of nonlinear equations can be highly sensitive to the initial guess of the solution. In this study, a new particle swarm optimization algorithm is proposed to solve systems of nonlinear equations. Some standard systems are presented to demonstrate the efficiency of this method.

[1]  I. K. Argyros.  On the solution of undetermined systems of nonlinear equations in Euclidean spaces , 1993 .

[2]  Stephen J. Wright,et al.  Numerical Optimization , 2018, Fundamental Statistical Inference.

[3]  Noël Gastinel,et al.  Linear numerical analysis , 1973 .

[4]  Sonia Krzyworzcka,et al.  Extension of the Lanczos and CGS methods to systems of nonlinear equations , 1996 .

[5]  Arieh Iserles,et al.  Approximation theory and optimization - tributes to M. J. D. Powell , 2009 .

[6]  A. Holstad.  Numerical solution of nonlinear equations in chemical speciation calculations , 1999 .

[7]  G. Nedzhibov.  A family of multi-point iterative methods for solving systems of nonlinear equations , 2008 .

[8]  Guojin Tang,et al.  Hybrid approach for solving systems of nonlinear equations using chaos optimization and quasi-Newton method , 2008, Appl. Soft Comput..

[9]  A. M. Chervyakov,et al.  General solutions of nonlinear equations in the geometric theory of the relativistic string , 1982 .

[10]  Qin Wang,et al.  Conjugate direction particle swarm optimization solving systems of nonlinear equations , 2009, Comput. Math. Appl..

[11]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[12]  Masao Iwamatsu,et al.  Locating All the Global Minima Using Multi-Species Particle Swarm Optimizer: The Inertia Weight and The Constriction Factor Variants , 2006, 2006 IEEE International Conference on Evolutionary Computation.

[13]  Zhi Wei Wan,et al.  Nonlinear numerical analysis of SRC Frame Joint , 2013 .

[14]  Juan R. Torregrosa,et al.  Modified Newton's method for systems of nonlinear equations with singular Jacobian , 2009 .

[15]  Karol Kowalski,et al.  Towards Complete Solutions to Systems of Nonlinear Equations of Many-Electron Theories , 1998 .

[16]  Katya Scheinberg,et al.  On the convergence of derivative-free methods for unconstrained optimization , 1997 .

[17]  M. El-Hawary,et al.  Enhancing the particle swarm optimizer via proper parameters selection , 2002, IEEE CCECE2002. Canadian Conference on Electrical and Computer Engineering. Conference Proceedings (Cat. No.02CH37373).

[18]  James Kennedy,et al.  Particle swarm optimization , 2002, Proceedings of ICNN'95 - International Conference on Neural Networks.

[19]  Kiselev,et al.  Stationary and moving intrinsic localized modes in one-dimensional monatomic lattices with cubic and quartic anharmonicity. , 1993, Physical review. B, Condensed matter.

[20]  R. Eberhart,et al.  Comparing inertia weights and constriction factors in particle swarm optimization , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[21]  Xiwen Lu,et al.  A new backtracking inexact BFGS method for symmetric nonlinear equations , 2008, Comput. Math. Appl..