The Barycenter Method for Direct Optimization: an Overview

TL;DR

This paper presents an overview of the barycenter method for derivative-free optimization, highlighting its robustness, parallelizability, and applicability to non-convex, non-smooth, and noisy functions, especially in control applications.

Contribution

It introduces a complex version of the barycenter method to improve performance and provides an overview of its properties and advantages in optimization tasks.

Findings

Robustness under noisy measurements

Parallelizable in a natural way

Applicable to non-convex and non-smooth functions

Abstract

A randomized version of the recently developed barycenter method for derivative--free optimization has desirable properties of a gradient search. We developed a complex version to avoid evaluations at high--gradient points. The method, which is also applicable to non--convex and to non--smooth functions, is parallelizable in a natural way and shown to be robust under noisy measurements. The goal of this paper is to present an overview of the method, whose properties make it particularly useful in control applications.