• 论文 •

### 一类带非单调线搜索的信赖域算法

1. 首都师范大学数学科学学院, 北京 100048
• 收稿日期:2009-06-01 出版日期:2011-02-15 发布日期:2011-03-08
• 基金资助:

国家自然科学基金(No. 60972140) 资助.

Pang Shanmin, Chen Lanping. A NEW FAMILY OF TRUST REGION ALGORITHMS WITH A NONMONOTONE LINE SEARCH TECHNIQUE[J]. Mathematica Numerica Sinica, 2011, 33(1): 48-56.

### A NEW FAMILY OF TRUST REGION ALGORITHMS WITH A NONMONOTONE LINE SEARCH TECHNIQUE

Pang Shanmin, Chen Lanping

1. School of Mathematical Sciences, Capital Normal University, Beijing 100048, China
• Received:2009-06-01 Online:2011-02-15 Published:2011-03-08

We propose a new family of trust region algorithms for unconstrained optimization problems which is combining traditional trust region method with a nonmonotone Wolfe line search technique. The new algorithm solves the trust region subproblem only once at each iteration, furthermore, the matrix approximation to the Hessian simultaneously satisfies the quasi-Newton condition at each iteration and maintains its positive definiteness. Under certain conditions, the global convergence and strong global convergence of the algorithm are proved. Numerical results show that the algorithm inherits the advantages of the nonmonotone schemes and is meaningful to some optimization problems.

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