A clustering heuristic to improve a derivative-free algorithm for nonsmooth optimization

TL;DR

This paper introduces a clustering heuristic to enhance a derivative-free method for nonsmooth optimization, leveraging Clarke's generalized gradient to find better descent directions, demonstrated through numerical experiments.

Contribution

The paper presents a novel clustering-based heuristic that improves the performance of the CS-DFN derivative-free optimization algorithm for nonsmooth problems.

Findings

The heuristic provides better descent directions in numerical tests.

Improved algorithm outperforms original CS-DFN on benchmark problems.

Numerical results validate the effectiveness of the proposed method.

Abstract

In this paper we propose an heuristic to improve the performances of the recently proposed derivative-free method for nonsmooth optimization CS-DFN. The heuristic is based on a clustering-type technique to compute a direction { which relies on an estimate of Clarke's generalized gradient} of the objective function. As such, this direction (as it is shown by the numerical experiments) is a good descent direction for the objective function. We report some numerical results and comparison with the original CS-DFN method to show the utility of the proposed improvement on a set of well-known test problems.