Affiliation:
1. School of Science Department of Mathematics, Zhejiang Sci‐Tech University Hangzhou China
2. School of Finance Zhejiang University of Finance and Economics Hangzhou China
3. School of Mathematics Liaoning Normal University Dalian China
Abstract
AbstractConjugate gradient methods are much effective for large‐scale unconstrained optimization problems by their simple computations and low memory requirements. The Perry conjugate gradient method has been considered to be one of the most efficient methods in the context of unconstrained minimization. However, a globally convergent result for general functions has not been established yet. In this paper, an improved three‐term Perry‐type algorithm is proposed which automatically satisfies the sufficient descent property independent of the accuracy of line search strategy. Under the standard Wolfe line search technique and a modified secant condition, the proposed algorithm is globally convergent for general nonlinear functions without convexity assumption. Numerical results compared with the Perry method for stability, two modified Perry‐type conjugate gradient methods and two effective three‐term conjugate gradient methods for large‐scale problems up to 300,000 dimensions indicate that the proposed algorithm is more efficient and reliable than the other methods for the testing problems. Additionally, we also apply it to some image restoration problems.
Funder
National Natural Science Foundation of China
Zhejiang University of Science and Technology
Reference48 articles.
1. Methods of conjugate gradients for solving linear systems;Hestenes R;J Res Natl Bureau Standards,1952
2. The conjugate gradient method in extreme problems;Polak E;Ussr Comput Math Math Phys,1969
3. Note sur la convergence de méthodes de directions conjugées;Polak E;Rev Franaise Informat Recherche Opérationnelle,1969
4. Function minimization by conjugate gradients;Fletcher R;Comput J,1964
5. A nonlinear conjugate gradient method with a strong global convergence property;Dai Y;SIAM J Optim,1999