A Scalar Modification of Three-term PRP-DL Conjugate Gradient Method for Solving Large-scaled Unconstrained Optimization Problems

Abstract

Unconstrained optimization problems arise in numerous fields. This study presents the introduction of a hybrid Polak Ribi‘ere-Polyak(PRP)-Dai-Liao(DL) conjugate gradient(CG) method with a modified scalar for the purpose of solving large -scaled unconstrained optimization problems. The proposed method involves the modification of the scalar in the PRP-DL conjugate gradient method in order to improve the performance of the algorithm, specifically when addressing large-scale problems. The convergence analysis of the proposed method is established and proved under the strong Wolfe-Powell line search. Numerical results on various test functions show that the proposed method is more efficient and robust than several existing CG methods. Overall, the proposed method is a new promising CG method for solving unconstrained optimization problems.