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We study novel robust zero-order algorithms with acceleration for thesolution of real-time optimization problems. In particular, we propose a familyof extremum seeking dynamics that can be universally modeled as singularlyperturbed hybrid dynamical systems with restarting mechanisms. From this familyof dynamics, we synthesize four fast algorithms for the solution of convex,strongly convex, constrained, and unconstrained optimization problems. In eachcase, we establish robust semi-global practical asymptotic or exponentialstability results, and we show how to obtain well-posed discretized algorithmsthat retain the main properties of the original dynamics. Given that existingaveraging theorems for singularly perturbed hybrid systems are not directlyapplicable to our setting, we derive a new averaging theorem that relaxes someof the assumptions made in the literature, allowing us to make a clear linkbetween the KL bounds that characterize the rates of convergence of the hybriddynamics and their average dynamics. We also show that our results areapplicable to non-hybrid algorithms, thus providing a general framework foraccelerated dynamics based on averaging theory. We present different numericalexamples to illustrate our results.

Robust Hybrid Zero-Order Optimization Algorithms with Acceleration via Averaging in Time