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Abstract
Solving systems of nonlinear equations is a very important task since the problems emerge mostly through the mathematical modelling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a self-adaptive combination of a metaheuristic with a classical local search method is able to converge to some difficult problems that are not solved by Newton-type methods.
Acknowledgements
The authors thank an anonymous referee and the editor whose comments and suggestions helped to improve the paper. This research has been supported by CIDEM (Centre for Research & Development in Mechanical Engineering, Portugal), FCT – Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) Project PEst-OE/EME/UI0615/2011, FEDER COMPETE (Programa Operacional Fatores de Competitividade/Operational Programme Thematic Factors of Competitiveness) and FCT Project FCOMP-01-0124-FEDER-022674.