新非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法

GLOBAL CONVERGENCE RESULTS OF LAMPARIELLO MODIFIED DIAGONAL-SPARSE QUASI-NEWTON METHOD WITH NEW NON-MONOTONE STEP SIZE RULE

本文设计了求解无约束最优化问题的新的非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法.新的步长规则类似于Grippo非单调线搜索规则并包含Grippo非单调线搜索规则作为特例.新的步长规则在每一次线搜索时得到一个相对于Grippo非单调线搜索规则的较大步长,同时保证算法的全局收敛性.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 of a Lampariello modified diagonal-sparse quasi-Newton method. The new step size rule is similar to the Grippo 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. Numerical results show that the new algorithms are efficient.