关于无约束规划的一个ODE算法的收敛性质

1.引言 所谓无约束规划的ODE算法,就是沿着一个常微分方程组初值问题的解曲线寻找光滑函数f(x)(x∈R~n)的极值点。这类方法近来很受重视,许多人对之进行了研究,见1]中所列文献。1]对现有的各种ODE方法进行了总结,并通过大量的数值试验对多种ODE方法以及两个公认的好的传统方法(一个是拟牛顿法,另一个是修正牛顿法)进

ON THE CONVERGENCE PROPERTIES OF AN ODE ALGORTHM FOR UNCONSTRAINED OPTIMIZATION

In this paper, we study the convergence properties of an ODE algorithm for uncon- strained optimization which is called IMPBOT in 1]. The global convergence and super- linear convergence of IMPBOT are proved. It is also shown by an example that the order of convergence is not larger than 1. This paper solves one of the problems proposed in 1].