Quantum mechanics

Algorithm

Conjugate

Derivation of the conjugate gradient method

Engineering

Aerospace engineering

Proximal Gradient Methods

Descent direction

Applied mathematics

Computer security

Nonlinear conjugate gradient method

Gradient descent

RADIUS

Gradient method

Computer science

Mathematical optimization

Physics

Line search

Descent (aeronautics)

Mathematics

Mathematical analysis

Artificial intelligence

Geometry

Conjugate residual method

Term (time)

Artificial neural network

Conjugate gradient method

Regular polygon

Machine learning

Convex function

Applied Numerical Mathematics

In this paper, a three-term conjugate gradient method with the new direction structure is proposed for solving large-scale unconstrained optimization problems, which generates a sufficient descent direction in per-iteration by the aid of some inexact line search conditions. Under suitable assumptions, the proposed method is globally convergent for nonconvex smooth problems. We further generalize the new direction structure to other traditional methods and obtain some algorithms with the same structure as the proposed method. Preliminary numerical comparisons show that the proposed methods are effective and promising for the test problems.

Some three-term conjugate gradient methods with the new direction structure