Nonlinear Conjugate Gradient Methods

Conjugate gradient methods are a class of important methods for solving linear equations and for solving nonlinear optimization. In this article, a review on conjugate gradient methods for unconstrained optimization is given. They are divided into early conjugate gradient methods, descent conjugate gradient methods, and sufficient descent conjugate gradient methods. Two general convergence theorems are provided for the conjugate gradient method assuming the descent property of each search direction. Some research issues on conjugate gradient methods are mentioned.

Keywords: conjugate gradient method; line search; descent property; sufficient descent condition; global convergence