Keywords : conjugate gradient algorithm

Investigation on Scaled CG-Type Algorithms for Unconstrained Optimization

Abbas Y. Al-Bayati; Khalil K. Abo; Salah G. Shareef

AL-Rafidain Journal of Computer Sciences and Mathematics, 2007, Volume 4, Issue 2, Pages 11-23
DOI: 10.33899/csmj.2007.164012

In this paper, we describe two new algorithms which are modifications of the Hestens-stiefl CG-method. The first is the scaled CG-method (obtained from function and gradient-values) which improves the search direction by multiplying to a scalar obtained from function value and its gradient at two successive points along the iterations. The second is the Preconditioned CG-method which uses an approximation at Hessein of the minimizing function. These algorithms are not sensitive to the line searches. Numerical experiments indicate that these new algorithms are effective and superior especially for increasing dimensionalities.

New Hybrid CG Algorithm Based on PR and FR Steps

Abbas Y. Al-Bayati; Khalil K. Abbo; Asma M. Abdalah

AL-Rafidain Journal of Computer Sciences and Mathematics, 2005, Volume 2, Issue 1, Pages 27-38
DOI: 10.33899/csmj.2005.164065

In this paper, a new hybrid conjugate gradient algorithm is proposed for unconstrained optimization. This algorithm combines the desirable computation aspects of Polak-Ribière steps and useful theoretical features of Fletcher-Reeves CG-steps. Computational results for this algorithm are given and compared with those of the Fletcher and Polak standard CG methods showing a considerable improvement over the latter two methods.