Physics

Mathematics

Economic growth

Term (time)

Line search

Financial economics

Algorithm

Mathematical optimization

Gradient method

Gradient descent

RADIUS

Artificial intelligence

Economics

Nonlinear conjugate gradient method

Convergence (economics)

Portfolio

Computer science

Quantum mechanics

Computer security

Artificial neural network

Conjugate gradient method

Selection (genetic algorithm)

AIMS Mathematics

&lt;abstract&gt;&lt;p&gt;The conjugate gradient (CG) method is an optimization method, which, in its application, has a fast convergence. Until now, many CG methods have been developed to improve computational performance and have been applied to real-world problems. In this paper, a new hybrid three-term CG method is proposed for solving unconstrained optimization problems. The search direction is a three-term hybrid form of the Hestenes-Stiefel (HS) and the Polak-Ribiére-Polyak (PRP) CG coefficients, and it satisfies the sufficient descent condition. In addition, the global convergence properties of the proposed method will also be proved under the weak Wolfe line search. By using several test functions, numerical results show that the proposed method is most efficient compared to some of the existing methods. In addition, the proposed method is used in practical application problems for image restoration and portfolio selection.&lt;/p&gt;&lt;/abstract&gt;

A new family of hybrid three-term conjugate gradient method for unconstrained optimization with application to image restoration and portfolio selection