关于不可微最优化的下降方法

ON DESCENT METHOD FOR NONDIFFERENTIABLE OPTIMIZATION

本文研究极小化局部 Lipschitz 连续函数的下降算法.文中给出了一个模型算法,它使用目标函数的近似广义梯度确定下降方向,这使得有可能构造仅使用函数值的不可微极小化下降算法.在适当的条件下,我们证明了算法的收敛性,并给出了有关此算法的若干数值计算结果.

This paper deals with descent algorithm for minimization of locally Lipschitz contin- uous functions.A model algorithm is given that employs approximate generalized gradi- ents of the objective function to determine the descent direction.This makes it possible to develp algorithm that merely use the function value.It is proved that the algorithm is convergent under suitable conditions.Numerical results of the algorithm is also present- ed.