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Mathematical Problems in Engineering
Volume 2015, Article ID 839659, 7 pages
http://dx.doi.org/10.1155/2015/839659
Research Article

A Spectral Dai-Yuan-Type Conjugate Gradient Method for Unconstrained Optimization

1Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2Huaibei Normal University, Huaibei 235000, China

Received 1 October 2015; Accepted 13 December 2015

Academic Editor: Paolo Maria Mariano

Copyright © 2015 Guanghui Zhou and Qin Ni. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new spectral conjugate gradient method (SDYCG) is presented for solving unconstrained optimization problems in this paper. Our method provides a new expression of spectral parameter. This formula ensures that the sufficient descent condition holds. The search direction in the SDYCG can be viewed as a combination of the spectral gradient and the Dai-Yuan conjugate gradient. The global convergence of the SDYCG is also obtained. Numerical results show that the SDYCG may be capable of solving large-scale nonlinear unconstrained optimization problems.