A new spectral conjugate gradient method for large-scale unconstrained optimization

作者：Jian, Jinbao^*; Chen, Qian; Jiang, Xianzhen; Zeng, Youfang; Yin, Jianghua

来源：Optimization Methods and Software, 2017, 32(3): 503-515.

DOI：10.1080/10556788.2016.1225213

• large-scale unconstrained optimization
• spectral conjugate gradient method
• global convergence
• numerical experiments
• 90C25
• 90C30

The spectral conjugate gradient methods, with simple construction and nice numerical performance, are a kind of effective methods for solving large-scale unconstrained optimization problems. In this paper, based on quasi-Newton direction and quasi-Newton condition, and motivated by the idea of spectral conjugate gradient method as well as Dai-Kou's selecting technique for conjugate parameter [SIAM J. Optim. 23 (2013), pp. 296-320], a new approach for generating spectral parameters is presented, where a new double-truncating technique, which can ensure both the sufficient descent property of the search directions and the bounded property of the sequence of spectral parameters, is introduced. Then a new associated spectral conjugate gradient method for large-scale unconstrained optimization is proposed. Under either the strong Wolfe line search or the generalized Wolfe line search, the proposed method is always globally convergent. Finally, a large number of comparison numerical experiments on large-scale instances from one thousand to two million variables are reported. The numerical results show that the proposed method is more promising.

• 出版日期2017-6
• 单位玉林师范学院; 广西大学