A Nonmonotone Filter Curvilinear Line Search Algorithm for Unconstrained Nonconvex Optimization

DOI：10.16205/j.cnki.cama.2017.0032

 作者 单位 E-mail 顾超 上海立信会计金融学院统计与数学学院, 上海 201620. guchao@lixin.edu.cn 朱德通 上海师范大学数学系, 上海 200234. dtzhu@shnu.edu.cn

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.

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.