A Hybrid Conjugate Gradient Algorithm for Nonlinear System of Equations through Conjugacy Condition

Abstract

the purpose of solving a large-scale system of nonlinear equations, a hybrid conjugate gradient algorithm is introduced in thispaper, based on the convex combination ofβFRkandβPRPkparameters. It is made possible by incorporating the conjugacy condition togetherwith the proposed conjugate gradient search direction. Furthermore, a significant property of the method is that through a non-monotone typeline search it gives a descent search direction. Under appropriate conditions, the algorithm establishes its global convergence. Finally, resultsfrom numerical tests on a set of benchmark test problems indicate that the method is more effective and robust compared to some existingmethods.