Nonsmooth trust-region algorithm with applications to robust stability of uncertain systems

TL;DR

This paper introduces a bundle trust-region algorithm designed for minimizing nonsmooth, nonconvex functions, with proven global convergence and demonstrated effectiveness on control problems.

Contribution

It presents a novel bundle trust-region method with convergence guarantees specifically tailored for nonsmooth, nonconvex optimization.

Findings

Proven global convergence of the proposed algorithm.

Classical trust-region convergence arguments do not hold in nonsmooth settings.

Experimental validation on automatic control problems shows effectiveness.

Abstract

We propose a bundle trust-region algorithm to minimize locally Lipschitz functions which are potentially nonsmooth and nonconvex. We prove global convergence of our method and show by way of an example that the classical convergence argument in trust-region methods based on the Cauchy point fails in the nonsmooth setting. Our method is tested experimentally on three problems in automatic control.