An algorithm for computing an element of the Clarke generalized Jacobian of a difference of max-type functions

TL;DR

This paper extends an existing algorithm to compute an element of the Clarke generalized Jacobian from max-type functions to a broader class of functions that are differences of max-type functions, enhancing its applicability.

Contribution

The authors generalize a known algorithm for Clarke Jacobian computation to include functions expressed as differences of max-type functions, broadening its utility.

Findings

Algorithm successfully extended to wider class of functions

Maintains computational efficiency for new function class

Applicable to more complex nonsmooth optimization problems

Abstract

We show that the algorithm for computing an element of the Clarke generalized Jacobian of a max-type function proposed by Zheng-da Huang and Guo-chun Ma can be extended to a much wider class of functions representable as a difference of max-type functions.