Estudo do Desempenho de Variações do Método de Cauchy para Minimização Irrestrita

Authors

  • S.A. Santos
  • L.O. Xavier

DOI:

https://doi.org/10.5540/tema.2005.06.01.0141

Abstract

No contexto de métodos para minimização irrestrita, são apresentadas uma nova proposta de direção e novas escolhas para o tamanho de passo no algoritmo de máxima descida. Estas propostas foram inspiradas nos trabalhos de Barzilai e Borwein (1988), Raydan e Svaiter (2002) e Dai, Yuan e Yuan (2002). Para a comparação entre os novos métodos e os clássicos, foram realizados testes com problemas quadráticos e de quadrados mínimos não lineares. A análise comparativa dos resultados foi feita pela técnica sugerida por Dolan e Moré (2002).

References

[1] J. Barzilai e J. Borwein, Two-point step size gradient methods, IMA J. Numer. Anal., 8 (1988), 141-148.

M.S. Bazaraa, H.D. Sherali e C.M. Shetty, “Nonlinear Programming: Theory and Algorithms”, 2 ed., John Wiley, New York, 1993.

A. Cauchy, Méthode générale pour la resolution des systems d’équations simultan ées, Comp. Rend. Sci Paris, 25 (1847), 536-538.

Y. Dai, J. Yuan e Y. Yuan, Modified Two-point stepsize gradient methods for unconstrained optimization, Comput. Optim. Appl., 22, No. 1 (2002), 103-109.

E.D. Dolan e J.J. Moré, Benchmarking optimization software with performance profiles, Math. Programming, 91 (2002), 201-213.

L. Grippo, F. Lampariello e S. Lucidi, A nonmonotone line search technique for Newton’s method, SIAM J. Numer. Anal., 23 (1986), 707-716.

J.J. Moré, B.S. Garbow e K.E. Hillstrom, Testing unconstrained optimization software, ACM Trans. Math. Software, 7 (1981), 17-41.

M. Raydan e B.F. Svaiter, Relaxed steepest descent and Cauchy-Barzilai- Borwein method, Comput. Optim. Appl., 21 (2002), 155-167.

S.A. Santos e L.O. Xavier, “Estudo do Desempenho de Métodos para Minimização Irrestrita com Controle de Passo”, Relatório de Pesquisa RP18/04, IMECC, Unicamp, Campinas, SP, abril 2004. Disponível em http://www.ime.unicamp.br/rel_pesq/2004/rp18-04.html.

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Published

2005-06-01

How to Cite

Santos, S., & Xavier, L. (2005). Estudo do Desempenho de Variações do Método de Cauchy para Minimização Irrestrita. Trends in Computational and Applied Mathematics, 6(1), 141–151. https://doi.org/10.5540/tema.2005.06.01.0141

Issue

Vol. 6 No. 1 (2005)

Section

Original Article

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