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一类带非单调线搜索的信赖域算法

庞善民, 陈兰平   

  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.

庞善民, 陈兰平. 一类带非单调线搜索的信赖域算法[J]. 计算数学, 2011, 33(1): 48-56.

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

通过将非单调 Wolfe 线搜索技术与传统的信赖域算法相结合, 我们提出了一类新的求解无约束最优化问题的信赖域算法.新算法在每一迭代步只需求解一次信赖域子问题, 而且在每一迭代步 Hesse 阵的近似都满足拟牛顿条件并保持正定传递.在一定条件下, 证明了算法的全局收敛性和强收敛性. 数值试验表明新算法继承了非单调技术的优点, 对于求解某些优化问题具有重要意义.

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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