A conjugate gradient algorithm for large-scale unconstrained optimization problems and nonlinear equations

• Main Authors: Gonglin Yuan, Wujie Hu
• Format: Article
• Language: English
• Published: SpringerOpen 2018-05-01
• Series: Journal of Inequalities and Applications
• Subjects: Conjugate gradient; Descent property; Global convergence
• Online Access: http://link.springer.com/article/10.1186/s13660-018-1703-1

Abstract For large-scale unconstrained optimization problems and nonlinear equations, we propose a new three-term conjugate gradient algorithm under the Yuan–Wei–Lu line search technique. It combines the steepest descent method with the famous conjugate gradient algorithm, which utilizes both the relevant function trait and the current point feature. It possesses the following properties: (i) the search direction has a sufficient descent feature and a trust region trait, and (ii) the proposed algorithm globally converges. Numerical results prove that the proposed algorithm is perfect compared with other similar optimization algorithms.