A Modified Algorithm of Finding an Element of Clarke Generalized Gradient for a Smooth Composition of Max-Type Functions
Year: 2000
Journal of Computational Mathematics, Vol. 18 (2000), Iss. 5 : pp. 513–520
Abstract
This paper refers to Clarke generalized gradient for a smooth composition of max-type functions of the form: $f(x)=g(x,\ {\rm max}_{j \in J_1} \ f_{1j}(x),\cdots, \ {\rm max}_{j \in J_m} \ f_{mj}(x))$, where $x\in R^n, \ J_i, \ i=1, ..., \ m$ are finite index sets, $g$ and $f_{ij}, \ j \in J_i, \ i=1,...,m$, are continuously differentiable on $R^{m+n}$ and $R^n$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2000-JCM-9062
Journal of Computational Mathematics, Vol. 18 (2000), Iss. 5 : pp. 513–520
Published online: 2000-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: Nonsmooth optimization Clarke generalized gradient Max-type function.