Abstract
We propose a new perspective for solving systems of nonlinear equations by viewing them as a multiobjective optimization problem where every equation represents an objective function whose goal is to minimize the difference between the right- and left-hand side of the corresponding equation of the system. An evolutionary computation technique is suggested to solve the problem obtained by transforming the system into a multiobjective optimization problem. Results obtained are compared with some of the well-established techniques used for solving nonlinear equation systems.
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References
Brezinski, C.: Projection methods for systems of equations. Elsevier, Amsterdam (1997)
Broyden, C.G.: A class of methods for solving nonlinear simultaneous equations. Mathematics of Computation 19, 577–593 (1965)
Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-Region methods. SIAM, Philadelphia (2000)
Cuyt, A., van der Cruyssen, P.: Abstract Pade approximants for the solution of a system of nonlinear equations. Comp. Math. and Appl. 9, 139–149 (1983)
Denis, J.E.: On Newton’s Method and Nonlinear Simultaneous Replacements. SIAM Journal of Numerical Analisys 4, 103–108 (1967)
Denis, J.E.: On Newton–like Methods. Numerical Mathematics 11, 324–330 (1968)
Denis, J.E.: On the Convergence of Broyden’s Method for Nonlinear Systems of Equations. Mathematics of Computation 25, 559–567 (1971)
Denis, J.E., Wolkowicz, H.: Least–Change Secant Methods, Sizing, and Shifting. SIAM Journal of Numerical Analisys 30, 1291–1314 (1993)
Denis, J.E., El-Alem, M., Williamson, K.: A Trust-Region Algorithm for Least-Squares Solutions of Nonlinear Systems of Equalities and Inequalities. SIAM Journal on Optimization 9(2), 291–315 (1999)
Effati, S., Nazemi, A.R.: A new methid for solving a system of the nonlinear equations. Applied Mathematics and Computation 168, 877–894 (2005)
Goldberg, D.E.: Genetic algorithms in search, optimization and machine learning. Addison Wesley, Reading (1989)
Gragg, W., Stewart, G.: A stable variant of the secant method for solving nonlinear equations. SIAM Journal of Numerical Analisys 13, 889–903 (1976)
Ortega, J.M., Rheinboldt, W.C.: Iterative solution of nonlinear equations in several variables. Academic Press, New York (1970)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge (2002)
Steuer, R.E.: Multiple Criteria Optimization. Theory, Computation, and Application. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons, New York (1986)
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Grosan, C., Abraham, A., Gelbukh, A. (2006). Evolutionary Method for Nonlinear Systems of Equations. In: Gelbukh, A., Reyes-Garcia, C.A. (eds) MICAI 2006: Advances in Artificial Intelligence. MICAI 2006. Lecture Notes in Computer Science(), vol 4293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11925231_27
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DOI: https://doi.org/10.1007/11925231_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-49026-5
Online ISBN: 978-3-540-49058-6
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