A MODIFIED ALGORITHM OF FINDING AN ELEMENT OFCLARKE GENERALIZED GRADIENT FOR A SMOOTHCOMPOSITION OF MAX-TYPE FUNCTIONS

• 来源期刊: 计算数学(英文版)
• 关键词: Nonsmooth optimization Clarke generalized gradient Max-type func- tion.
• 年，卷（期）: 2000,（5）
• 页码范围: 513-520
• 页数: 8页
• 语种: 英文

摘要

This paper refers to Clarke generalized gradient for a smooth composition of max-type functions of the form: f(x) = g(x, maxjej1 f1j(x),..., maxjeJm fmj(x) ), where x∈Rn, Ji, i = 1,.,m are finite index sets, g and fij,j ~ Ji, i = 1,. , m, are continuously differentiable on Rm+n and Rn, respectively. In a previous paper, we proposed an algorithm of finding an element of Clarke generalized gradient for f, at a point. In that paper, finding an element of Clarke generalized gradient for f, at a point, is implemented by determining the compatibilities of systems of linear inequalities many times. So its computational amount is very expensive. In this paper, we will modify the algorithm to reduce the times that the compatibilities of systems of linear inequalities have to be determined.