A Hybrid Conjugate Gradient Algorithm for Nonlinear System of Equations through Conjugacy Condition
DOI:
https://doi.org/10.61360/BoniGHSS242016851001Keywords:
conjugate gradient parameters, convex combination, conjugacy condition, global convergence, numerical experimentsAbstract
For the purpose of solving a large-scale system of nonlinear equations, a hybrid conjugate gradient algorithm is introduced in this paper, based on the convex combination of βFR k and βPRP k parameters. It is made possible by incorporating the conjugacy condition together with the proposed conjugate gradient search direction. Furthermore, a significant property of the method is that through a non-monotone type line search it gives a descent search direction. Under appropriate conditions, the algorithm establishes its global convergence. Finally, results from numerical tests on a set of benchmark test problems indicate that the method is more effective and robust compared to some existing methods.
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