Gene

Quantum mechanics

Algorithm

Engineering

Aerospace engineering

Applied mathematics

Computer security

Robustness (evolution)

Convergence (economics)

Gradient descent

RADIUS

Computation

Economics

Biochemistry

Computer science

Mathematical optimization

Physics

Line search

Descent (aeronautics)

Mathematics

Artificial intelligence

Geometry

Chemistry

Economic growth

Term (time)

Artificial neural network

Conjugate gradient method

Regular polygon

Machine learning

Convex function

Journal of Mathematics

A new modified three-term conjugate gradient (CG) method is shown for solving the large scale optimization problems. The idea relates to the famous Polak-Ribière-Polyak (PRP) formula. As the numerator of PRP plays a vital role in numerical result and not having the jamming issue, PRP method is not globally convergent. So, for the new three-term CG method, the idea is to use the PRP numerator and combine it with any good CG formula’s denominator that performs well. The new modification of three-term CG method possesses the sufficient descent condition independent of any line search. The novelty is that by using the Wolfe Powell line search the new modification possesses global convergence properties with convex and nonconvex functions. Numerical computation with the Wolfe Powell line search by using the standard test function of optimization shows the efficiency and robustness of the new modification.

A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence