A modified homogeneous algorithm for function minimization

Recently, an algorithm for function minimization was presented, based upon an homogeneous, rather than upon a quadratic, model. Numerical experiments with this algorithm indicated that it rapidly minimizes the standard test functions available in the literature. Although it was proved that the algor...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 46; no. 2; pp. 533 - 541
Main Authors Jacobson, D.H, Pels, L.M
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.1974
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Summary:Recently, an algorithm for function minimization was presented, based upon an homogeneous, rather than upon a quadratic, model. Numerical experiments with this algorithm indicated that it rapidly minimizes the standard test functions available in the literature. Although it was proved that the algorithm produces function values which continually descend, no proof of convergence was supplied. In this paper, the homogeneous algorithm is modified primarily by replacing the cubic interpolation routine by Armijo's step size rule. Although not quite as fast as the original version on the standard test functions, this modified form has the advantage that a proof of convergence follows from a general theorem of Polak.
ISSN:0022-247X
1096-0813
DOI:10.1016/0022-247X(74)90259-5