A New Hestenes-Stiefel and Fletcher-Reeves Conjugate Gradient Method with Descent Properties for Optimization Models

Document Type: Research Paper


1 Faculty of Informatics and Computing, Sultan Zainal Abidin University, Kuala Terengganu, Malaysia

2 Department of Mathematics, Faculty of Mathematics and Natural Science, Sam Ratulangi University, Indonesia

3 bDepartment of Mathematics, Faculty of Mathematics and Natural Science, Sam Ratulangi University, Indonesia


The conjugate gradient (CG) scheme is regarded as among the efficient methods for large-scale optimization problems. Several versions of CG methods have been presented recently owing to their rapid convergence, simplicity, and their less memory requirements. In this article, we construct a new CG algorithm via the combination of the classical methods of Fletcher-Reeves (FR), and Hestenes-Stiefel (HS). The new CG method possesses the descent properties and converge globally provided the exact minimization condition is satisfied. The tests of the new CG method using MATLAB are analysed in terms of iteration number and CPU time. Numerical results have been reported which shows that the proposed CG method performs better compare to other CG methods.


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