On the accelerating property of an algorithm for function minimization without calculating derivatives

Philippe Toint; Frank Callier

doi:10.1007/BF00933295

On the accelerating property of an algorithm for function minimization without calculating derivatives

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Résumé

This paper studies the speed of convergence of a general algorithm for function minimization without calculating derivatives. This algorithm contains Powell's 1964 algorithm as well as Zangwill's second modification of this procedure. The main results are Theorems 3.1 and 4.1 which show that, if the algorithm behaves well, then asymptotically almost conjugate directions are built; therefore, the algorithm has an every-iteration superlinear speed of convergence. The paper hinges on ideas of McCormick and Ritter and Powell.

langue originale	Anglais
Pages (de - à)	531-547
Nombre de pages	17
journal	Journal of Optimization Theory and Applications.
Volume	23
Numéro de publication	4
Les DOIs	https://doi.org/10.1007/BF00933295
Etat de la publication	Publié - 1 déc. 1977

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10.1007/BF00933295

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ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire
SARTENAER, A. & TOINT, P.
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abstract = "This paper studies the speed of convergence of a general algorithm for function minimization without calculating derivatives. This algorithm contains Powell's 1964 algorithm as well as Zangwill's second modification of this procedure. The main results are Theorems 3.1 and 4.1 which show that, if the algorithm behaves well, then asymptotically almost conjugate directions are built; therefore, the algorithm has an every-iteration superlinear speed of convergence. The paper hinges on ideas of McCormick and Ritter and Powell.",

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AB - This paper studies the speed of convergence of a general algorithm for function minimization without calculating derivatives. This algorithm contains Powell's 1964 algorithm as well as Zangwill's second modification of this procedure. The main results are Theorems 3.1 and 4.1 which show that, if the algorithm behaves well, then asymptotically almost conjugate directions are built; therefore, the algorithm has an every-iteration superlinear speed of convergence. The paper hinges on ideas of McCormick and Ritter and Powell.

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On the accelerating property of an algorithm for function minimization without calculating derivatives

Résumé

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ADALGOPT: ADALGOPT - Algorithmes avancés en optimisation non-linéaire

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