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Nonlinear Conjugate Gradient Methods

  1. Yu-Hong Dai

Published Online: 15 FEB 2011

DOI: 10.1002/9780470400531.eorms0183

Wiley Encyclopedia of Operations Research and Management Science

Wiley Encyclopedia of Operations Research and Management Science

How to Cite

Dai, Y.-H. 2011. Nonlinear Conjugate Gradient Methods. Wiley Encyclopedia of Operations Research and Management Science. .

Author Information

  1. Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science, Chinese Academy of Sciences, State Key Laboratory of Scientific and Engineering Computing, Beijing, P.R., China

Publication History

  1. Published Online: 15 FEB 2011

Abstract

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