• 论文 •

无约束优化问题的对角稀疏拟牛顿法

1. (1)曲阜师范大学运筹与管理学院, 山东日照 276826 (2)中国科学院数学与系统科学研究院计算数学与科学工程计算研究所, 北京 100080
• 收稿日期:2003-04-14 修回日期:2004-11-15 出版日期:2006-02-25 发布日期:2006-02-25

Shi Zhenjun;Sun Guo. A Diagonal-Sparse Quasi-Newton Method for Unconstrained Optimization Problem[J]. Journal of Systems Science and Mathematical Sciences, 2006, 26(1): 101-112.

A Diagonal-Sparse Quasi-Newton Method for Unconstrained Optimization Problem

Shi Zhenjun(1)(2), Sun Guo(1)

1. (1)School of Operations Research and Management Science, Qufu Normal University, Rizhao, Shandong276826 (2)
• Received:2003-04-14 Revised:2004-11-15 Online:2006-02-25 Published:2006-02-25

Armijo非精确线性搜索,并在每次迭代中利用对角矩阵近似拟牛顿法中的校正矩阵,使计算搜索

In this paper, we present a diagonal-sparse quasi-Newton method for
unconstrained optimization problems. The method is similar to
quasi-Newton method, but restricts the quasi-Newton matrix to a sparse matrix, and uses
approximate quasi-Newton condition to determine a search direction and uses Armijo's
line search rule to define a step-size at each iteration.
It avoids the storage and computation of
some matrices in its iteration, so that it is suitable for solving large scale optimization problems.
Under some mild assumptions, we prove
the global convergence and linear convergence
rate, and futher analyze the superlinear convergence property of this method.
Numerical experiments show that the diagonal-sparse
quasi-Newton method is suitable to solve large scale problems, especially the problems
in which the Hesse matrix of objective functions is sparse. Numerical results also show that
the new method is more efficient than other similar methods, such as Cauchy method, conjugate