Robust hybrid zero-order optimization algorithms with acceleration via averaging in time

Abstract This paper presents a new class of robust zero-order algorithms for the solution real-time optimization problems with acceleration. In particular, we propose family extremum seeking (ES) dynamics that can be universally modeled as singularly perturbed hybrid dynamical systems restarting mechanisms. From this dynamics, synthesize four fast convex, strongly constrained, and unconstrained problems. each case, establish semi-global practical asymptotic or exponential stability results, also show how to obtain well-posed discretized retain main properties original dynamics. Given existing averaging theorems are not directly applicable our setting, derive an extended theorem relaxes some assumptions made in literature, allowing us make clear link between K L bounds characterize rates convergence their average We results non-hybrid algorithms, thus providing general framework accelerated ES based on theory. present different numerical examples illustrate results.