A nonmonotone trust region method based on nonincreasing technique of, weighted average of the successive function values

作者：Mo, Jiangtao^*; Liu, Chunyan; Yan, Shicui

来源：Journal of Computational and Applied Mathematics, 2007, 209(1): 97-108.

DOI：10.1016/j.cam.2006.10.070

• unconstrained optimization problems
• nonmonotone line search
• nonmonotone trust region method
• global convergence
• superlinear convergence

In this paper we propose a nonmonotone trust region method. Unlike traditional nonmonotone trust region method, the nonmonotone technique applied to our method is based on the nonmonotone line search technique proposed by Zhang and Hager [A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim. 14(4) (2004) 1043-1056] instead of that presented by Grippo et al. [A nonmonotone line search technique for Newton's method, SIAM J. Numer. Anal. 23(4) (1986) 707-7161. So the method requires nonincreasing of a special weighted average of the successive function values. Global and superlinear convergence of the method are proved under suitable conditions. Preliminary numerical results show that the method is efficient for unconstrained optimization problems.

• 出版日期2007-12-1
• 单位广西大学