On a probabilistic global optimizer derived from the Walker slice sampling

TL;DR

This paper introduces SwiftNav, a probabilistic global optimization algorithm that uses adaptive discretization, Walker slice sampling, and simulated annealing to efficiently find global optima in high-dimensional, possibly non-convex functions.

Contribution

The paper presents SwiftNav, a novel zeroth order optimizer combining adaptive discretization, Walker slice sampling, and simulated annealing for high-dimensional global optimization.

Findings

Effective in high-dimensional benchmark problems

Parallelizable for scalability

Accurately identifies global optimizers

Abstract

This article presents a zeroth order probabilistic global optimization algorithm -- SwiftNav -- for (not necessarily convex) functions over a compact domain. A discretization procedure is deployed on the compact domain, starting with a small step-size $h > 0$ and subsequently adaptively refining it in the course of a simulated annealing routine utilizing the Walker slice and the Gibbs sampler, in order to identify a set of global optimizers up to good precision. SwiftNav is parallelizable, which helps with scalability as the dimension of decision variables increases. Several numerical experiments are included here to demonstrate the effectiveness and accuracy of SwiftNav in high-dimensional benchmark optimization problems.