TY - JOUR
T1 - A Direct Search Frame-Based Conjugate Gradients Method
AU - I. D. Coope & C. J. Price 
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 - <p style="text-align: justify;">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.</p>