极小化一元凸函数的一个数值方法

本文给出了一个极小化一元非光滑凸函数的可执行的数值方法，此算法的要点是仅用在已有的五个点上的函数值去确定两个更好的接近最优解的点．我们证明了这个算法是全局收敛的和ｒ－超线性收敛的，数值结果也表明此算法有好的收敛性．

A NUMERICAL METHOD FOR UNIVARIATE MINIMIZATION OF CONVEX FUNCTION

This paper presents an implementable numerical minimixation algorithm for one-dimensional convex nonsmooth functions. The main feature of the iterative algorithm is that only the function values at five preceding points are employed to determine two new better approximate points. Global convergence of the algorithm is proved. If objective function satisfies a certain condition, the algorithm is r - superlinear convergent. Numerical results also show the desired convergence property of the method.