Uniform non-convex optimisation via Extremum Seeking

TL;DR

This paper analyzes a well-known extremum seeking scheme, demonstrating its uniformity and stability properties, and showing it can reliably find the global minimum even in non-convex landscapes with local minima.

Contribution

The paper proves uniformity properties of extremum seeking schemes and demonstrates their ability to ensure global minimizer stability in non-convex optimization.

Findings

Guarantees global minimizer semi-global practical stability

Shows improved scheme with high-pass filter achieves global stability

Establishes uniformity with respect to dither amplitude and cost function

Abstract

The paper deals with a well-known extremum seeking scheme by proving uniformity properties with respect to the amplitudes of the dither signal and of the cost function. Those properties are then used to show that the scheme guarantees the global minimiser to be semi-global practically stable despite the presence of local minima. Under the assumption of a globally Lipschitz cost function, it is shown that the scheme, improved through a high-pass filter, makes the global minimiser practically stable with a global domain of attraction.