Conjugate

Derivation of the conjugate gradient method

Applied mathematics

Nonlinear conjugate gradient method

Convergence (economics)

Gradient descent

Gradient method

Economics

Computer science

Mathematical optimization

Scalar (mathematics)

Mathematics

Mathematical analysis

Artificial intelligence

Geometry

Conjugate residual method

Economic growth

Artificial neural network

Conjugate gradient method

计算数学：英文版

The conjugate gradient method for unconstrained optimization problems varies with a scalar. In this note, a general condition concerning the scalar is given, which ensures the global convergence of the method in the case of strong Wolfe line searches. It is also discussed how to use the result to obtain the convergence of the famous Fletcher-Reeves, and Polak-Ribiere-Polyak conjugate gradient methods. That the condition cannot be relaxed in some sense is mentioned.

A NOTE ON THE NONLINEAR CONJUGATE GRADIENT METHOD