Multiple Roots of Systems of Equations by Repulsion Merit Functions
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 do...
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| Other Authors: | , |
| Format: | article |
| Language: | eng |
| Published: |
2015
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10400.22/5409 |
| Country: | Portugal |
| Oai: | oai:recipp.ipp.pt:10400.22/5409 |
| Summary: | 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. |
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