一种求解无约束极值问题的无记忆拟牛顿算法

A MEMORYLESS QUASI-NEWTON METHOD FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS

§1.引言 求无约束极值常用的方法,有CG算法、变尺度算法以及拟牛顿算法等等.变尺度算法虽然收敛速度快,但是存贮量大(为O(n^2))。CG算法所需存贮量(为O(n))虽小,但在收敛速度上一般不如变尺度法.因此,本文探索收敛速度快且所需存贮量小的算法。

This paper gives a Quasi-Newton method which does not do matrix calculus for a newiteration point. Its convergence is proved. Numerical test shows that the convergence is veryfast for a fixed step algorithm. To get a new iteration point by the fixed step algorithm, thefunctional value is computed once. This method provides a new way for solving large scaleunconstrained optimization problems.