Volume 22, Issue 4
A Direct Search Frame-Based Conjugate Gradients Method

J. Comp. Math., 22 (2004), pp. 489-500.

Published online: 2004-08

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• Abstract

A derivative-free frame-based conjugate gradients algorithm is presented. Convergence is shown for $C^1$ functions, and this is verified in numerical trials. The algorithm is tested on a variety of low dimensional problems, some of which are ill-conditioned, and is also tested on problems of high dimension. Numerical results show that the algorithm is effective on both classes of problems. The results are compared with those from a discrete quasi-Newton method, showing that the conjugate gradients algorithm is competitive. The algorithm exhibits the conjugate gradients speed-up on problems for which the Hessian at the solution has repeated or clustered eigenvalues. The algorithm is easily parallelizable.

• Keywords

Conjugate gradients, Derivative-free, Frame-based methods, Numerical results.

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@Article{JCM-22-489, author = {}, title = {A Direct Search Frame-Based Conjugate Gradients Method}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {4}, pages = {489--500}, abstract = {

A derivative-free frame-based conjugate gradients algorithm is presented. Convergence is shown for $C^1$ functions, and this is verified in numerical trials. The algorithm is tested on a variety of low dimensional problems, some of which are ill-conditioned, and is also tested on problems of high dimension. Numerical results show that the algorithm is effective on both classes of problems. The results are compared with those from a discrete quasi-Newton method, showing that the conjugate gradients algorithm is competitive. The algorithm exhibits the conjugate gradients speed-up on problems for which the Hessian at the solution has repeated or clustered eigenvalues. The algorithm is easily parallelizable.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8858.html} }
TY - JOUR T1 - A Direct Search Frame-Based Conjugate Gradients Method JO - Journal of Computational Mathematics VL - 4 SP - 489 EP - 500 PY - 2004 DA - 2004/08 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8858.html KW - Conjugate gradients, Derivative-free, Frame-based methods, Numerical results. AB -

A derivative-free frame-based conjugate gradients algorithm is presented. Convergence is shown for $C^1$ functions, and this is verified in numerical trials. The algorithm is tested on a variety of low dimensional problems, some of which are ill-conditioned, and is also tested on problems of high dimension. Numerical results show that the algorithm is effective on both classes of problems. The results are compared with those from a discrete quasi-Newton method, showing that the conjugate gradients algorithm is competitive. The algorithm exhibits the conjugate gradients speed-up on problems for which the Hessian at the solution has repeated or clustered eigenvalues. The algorithm is easily parallelizable.

I. D. Coope & C. J. Price . (1970). A Direct Search Frame-Based Conjugate Gradients Method. Journal of Computational Mathematics. 22 (4). 489-500. doi:
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