A Robust Control Approach to Asymptotic Optimality of the Heavy Ball Method for Optimization of Quadratic Functions

Autor:	Ugrinovskii, V., Petersen, I. R., Shames, I.
Rok vydání:	2023
Předmět:	Mathematics - Optimization and Control Electrical Engineering and Systems Science - Systems and Control
Druh dokumentu:	Working Paper
Popis:	Among first order optimization methods, Polyak's heavy ball method has long been known to guarantee the asymptotic rate of convergence matching Nesterov's lower bound for functions defined in an infinite-dimensional space. In this paper, we use results on the robust gain margin of linear uncertain feedback control systems to show that the heavy ball method is provably worst-case asymptotically optimal when applied to quadratic functions in a finite dimensional space. Comment: Accepted for publication in Automatica
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2305.06593 Zobrazit plný text záznamu View this record from Arxiv