Algorithm

Conjugate

Applied mathematics

Computer security

Gradient descent

RADIUS

Computation

Computer science

Mathematical optimization

Physics

Line search

Descent (aeronautics)

Mathematics

Mathematical analysis

Artificial intelligence

Geometry

Meteorology

Artificial neural network

Conjugate gradient method

Line (geometry)

Mathematical Problems in Engineering

Conjugate gradient (CG) method is an interesting tool to solve optimization problems in many fields, such as design, economics, physics, and engineering. In this paper, we depict a new hybrid of CG method which relates to the famous Polak-Ribière-Polyak (PRP) formula. It reveals a solution for the PRP case which is not globally convergent with the strong Wolfe-Powell (SWP) line search. The new formula possesses the sufficient descent condition and the global convergent properties. In addition, we further explained about the cases where PRP method failed with SWP line search. Furthermore, we provide numerical computations for the new hybrid CG method which is almost better than other related PRP formulas in both the number of iterations and the CPU time under some standard test functions.

An Efficient Hybrid Conjugate Gradient Method with the Strong Wolfe-Powell Line Search