One dimensional consensus based algorithm for non-convex optimization

TL;DR

This paper provides a rigorous quantitative analysis of a one-dimensional consensus-based optimization method, establishing error estimates between the consensus point and the global minimum without assuming specific structural properties of the objective function.

Contribution

It offers the first comprehensive error estimate for the one-dimensional consensus-based optimization method applicable to general objective functions.

Findings

Established quantitative error bounds between consensus point and global minimizer.

Validated the method's effectiveness for a broad class of objective functions.

Provided theoretical guarantees without structural assumptions.

Abstract

We analyze the consensus based optimization method proposed by Pinnau et al.(2017) in one dimension. We rigorously provide a quantitative error estimate between the consensus point and global minimizer of a given objective function. Our analysis covers general objective functions; we do not require any structural assumption on the objective function.