Line Search Methods in Conjugate Gradient Algorithms: A study of nonlinear unconstrained optimization problems

Nonlinear conjugate gradient methods (CG) are especially efficient methods for the solution of the large scale unconstrained optimization problems, as these methods are characterized by low memory requirement and strong local and global convergence properties. However, line search in CG methods is of critical importance. Reducing line search cost in conjugate gradient algorithm is the main objective of this monograph. Based on the type of the line searches applied in the CG method, these methods are generally divided into three approaches. The conjugate gradient methods with exact line search, inexact line search and conjugate gradient without any line search. This study is intended to compare and analyze the efficiency and effectiveness of these optimization techniques through numerical simulations.