Multiple Roots of Systems of Equations by Repulsion Merit Functions

• Autor(a) principal: Ramadas, Gisela C. V.
• Data de Publicação: 2014
• Outros Autores: Fernandes, Edite M. G. P., Rocha, Ana Maria A. C.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10400.22/5409
• topic: System of equations; Multiple roots; Penalty function; Repulsion; Harmony search

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several iterations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.