On the sufficient descent condition of the Hager-Zhang conjugate gradient methods
Conjugate gradient (CG) methods comprise a class of unconstrained optimization algorithms characterized by low memory requirements and strong global convergence properties. Although CG methods are not the fastest or most robust optimization algorithms available today, they remain very popular for engineers and mathematicians engaged in solving large-scale problems in the following form: \(\underset{x \in \mathbb R^n}\min f (x)\), where \(f : \mathbb R^n \to \mathbb R\) is a smooth nonlinear function and its gradient is available. Based on an eigenvalue study, the author establishes the sufficient descent condition of an extended class of the Hager-Zhang nonlinear conjugate gradient methods.
Hager-Zhang nonlinear conjugate gradient method
scientific article; zbMATH DE number 6381324
scientific article