大步长非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法的全局收敛性

Global Convergence Results of Lampariello Modified Diagonal-sparse Quasi-Newton Method With Larger Non-monotone-step Size Rule

本文在Zhang H.C.的非单调线搜索规则基础上,结合Shi Z.J.大步长线搜索技巧提出了新的大步长的非单调线搜索规则,设计了求解无约束最优化问题的大步长非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法,在▽f(x)一致连续的条件下给出了算法的全局收敛性和超线性收敛性分析.数值例子表明算法是有效的,适合求解大规模问题.

We propose a new non-monotone step size rule and analyze the global convergence and convergence rate of a Lampariello modified diagonal-sparse quasi-Newton method. The new step size rule is similar to the Zhang H. C non-monotone step size rule and contains it as a special case. We can choose a larger stepsize in each line search procedure and maintain the global convergence property of our Lampariello modified diagonal-sparse quasi-Newton method under the assumption that △f（x） is uniformly continuous, and further analyze the superlinear convergence property of the new method. Numerical results show that the new method is efficient and suitable to solve large scale problems.