无记忆非拟 Newton 算法的导出和全局收敛性

Derivation and Global Convergence for Memoryless Non-quasi-Newton Method

中文关键词:  无记忆非拟Newton公式  Wolfe线搜索  全局收敛性.

英文关键词:memoryless non-quasi-Newton method  Wolfe line search  global convergence.

中文摘要:

      本文导出了一类无记忆非拟 Newton 公式, 并证明了采用非精确线搜索的无记忆非拟 Newton算法的全局收敛性. 文中还将无记忆非 拟 Newton 公式 和Perry-Shanno无记忆拟牛顿公式相结合, 提出了一种混合无记忆非拟牛顿校正 公式, 并在较弱条件下证明了混合无记忆非拟 Newton 算法在Wolfe 线搜索下具有全局收敛性. 测试函数的计算表明, 文中提出的两种算法是有效的. 特别是无记忆非拟 Newton 算法, 所需存储量及计算量较小, 更适合求解大规模无约束优化问题.

英文摘要:

      In this paper, a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved. Furthermore, we propose a hybrid method that mixes both the memoryless non-quasi-Newton method and the memoryless Perry-Shanno quasi-Newton method. The global convergence of this hybrid memoryless method is proved under mild assumptions. The initial results show that these new methods are efficient for the given test problems. Especially the memoryless non-quasi-Newton method requires little storage and computation, so it is able to efficiently solve large scale optimization problems.