Desempenho do método de Newton truncado em optimização não linear sem restrições

Ana I.P.N. Pereira *

Edite M.G.P. Fernandes †

* Departamento de Matemática, Instituto Politécnico de Bragança

apereira@ipb.pt

† Departamento de Produção e Sistemas, Universidade do Minho

emgpf@dps.uminho.pt

Title: Performance of the truncated Newton method in unconstrained nonlinear optimization

Abstract:

Newton's method for unconstrained nonlinear optimization can be a demanding iterative process. Combining Krylov iterative methods with different termination criteria for the inexact solving of the Newton system, a linear or a curvilinear search technique and monotone and nonmonotone globalization criteria, we manage to define a set of truncated Newton algorithms. Computational experiments were carried out in order to evaluate the performance of the defined algorithms.

Keywords: Unconstrained optimization, truncated Newton's method, nonmonotone stabilization technique.

Resumo:

O método de Newton para a resolução de um problema de optimização não linear sem restrições pode originar um processo iterativo exigente. Combinando métodos iterativos de Krylov com diferentes critérios de terminação para a resolução inexacta do sistema Newton, uma técnica de procura que pode ser linear ou curvilínea e critérios de globalização monótonos e não monótonos, conseguimos definir um conjunto de algoritmos do método de Newton truncado. Foram realizadas experiências computacionais para avaliar o desempenho dos diferentes algoritmos.

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