Performance Analysis of Parameters of Classical Conjugate Gradient Methods Using Armijo Line Search
Michael Oluwaseun Ayansiji *
Department of Industrial Mathematics, Admiralty University of Nigeria, Ibusa, Delta State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The Conjugate Gradient (CG) method is widely used for solving large-scale unconstrained optimization problems due to its efficiency and low memory requirements. However, its performance depends significantly on the choice of update parameters and line search strategies. This study evaluates eight classical CG methods using the Armijo line search framework, assessing their convergence rates, accuracy, and computational performance through extensive numerical experiments on benchmark optimization problems. The results indicate that the PRP, LS, HZ, and FR methods exhibit superior efficiency in solving large-scale nonlinear problems. These findings contribute to the understanding of CG method behavior and offer insights into selecting appropriate update parameters for practical applications.
Keywords: Conjugate gradient methods, Armijo line search, large-scale optimization, unconstrained optimization, performance profiling