| 顾超,朱德通.非单调滤子曲率线搜索算法解无约束非凸优化[J].数学年刊A辑,2017,38(4):391~404 |
| 非单调滤子曲率线搜索算法解无约束非凸优化 |
| A Nonmonotone Filter Curvilinear Line Search Algorithm for Unconstrained Nonconvex Optimization |
| Received:September 29, 2015 Revised:September 06, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0032 |
| 中文关键词: Nonconvex optimization, Nonmonotone, Curvilinear line search, Filter, Convergence |
| 英文关键词:Nonconvex optimization, Nonmonotone, Curvilinear line search, Filter, Convergence |
| 基金项目:本文受到国家自然科学基金(No.11201304,No.11371253),上海市自然科学基金和上海立信会计金融学院统计学一级学科项目的资助. |
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| 中文摘要: |
| 宇和濮在文[Yu Z S, Pu D G. A new nonmonotone line search technique for unconstrained optimization
[J]. {\it J Comput Appl Math}, 2008, 219:134--144]
中提出了一种非单调的线搜索算法解无约束优化问题.
和他们的工作不同, 当优化问题非凸时, 本文给出了一种非单调滤子曲率线搜索算法.
通过使用海森矩阵的负曲率信息, 算法产生的迭代序列被证明收敛于一个满足二阶充分性条件的点.
在不需要假设极限点存在的情况下, 证明了算法具有整体收敛性.
而且分析了该算法的收敛速率. 数值试验表明算法的有效性. |
| 英文摘要: |
| Yu and Pu [Yu Z S, Pu D G. A new nonmonotone line search technique for unconstrained optimization
[J]. {\it J Comput Appl Math}, 2008, 219:134--144] introduced a
nonmonotone line search algorithm for unconstrained optimization.
Different from their work, the authors propose a nonmonotone filter
curvilinear line search algorithm when a problem may be nonconvex.
By using the negative curvature information of the Hessian, the
generated sequence is shown to converge to stationary points that
satisfy second-order optimality conditions. Global convergence is
established even without requiring a priori the existence of a
limit point. Moreover, the authors analyze the convergence rate of
the new algorithm. The numerical experiments are reported to show
the effectiveness of the proposed algorithm. |
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