Global Convergence and Asymptotic Optimality of the Heavy Ball Method for a Class of Nonconvex Optimization Problems

V. Ugrinovskii; I. R. Petersen; I. Shames

doi:10.1109/LCSYS.2022.3163408

Global Convergence and Asymptotic Optimality of the Heavy Ball Method for a Class of Nonconvex Optimization Problems

V. Ugrinovskii, I. R. Petersen, I. Shames^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

In this letter we revisit the famous heavy ball method and study its global convergence for a class of non-convex problems with sector-bounded gradient. We characterize the parameters that render the method globally convergent and yield the best R-convergence factor. We show that for this family of functions, this convergence factor is superior to the factor obtained from the triple momentum method.

Original language	English
Pages (from-to)	2449-2454
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	6
DOIs	https://doi.org/10.1109/LCSYS.2022.3163408
Publication status	Published - 2022

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title = "Global Convergence and Asymptotic Optimality of the Heavy Ball Method for a Class of Nonconvex Optimization Problems",

abstract = "In this letter we revisit the famous heavy ball method and study its global convergence for a class of non-convex problems with sector-bounded gradient. We characterize the parameters that render the method globally convergent and yield the best R-convergence factor. We show that for this family of functions, this convergence factor is superior to the factor obtained from the triple momentum method.",

keywords = "Optimization algorithms, robust control",

author = "V. Ugrinovskii and Petersen, {I. R.} and I. Shames",

note = "Publisher Copyright: {\textcopyright} 2017 IEEE.",

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AU - Ugrinovskii, V.

AU - Petersen, I. R.

AU - Shames, I.

PY - 2022

Y1 - 2022

N2 - In this letter we revisit the famous heavy ball method and study its global convergence for a class of non-convex problems with sector-bounded gradient. We characterize the parameters that render the method globally convergent and yield the best R-convergence factor. We show that for this family of functions, this convergence factor is superior to the factor obtained from the triple momentum method.

AB - In this letter we revisit the famous heavy ball method and study its global convergence for a class of non-convex problems with sector-bounded gradient. We characterize the parameters that render the method globally convergent and yield the best R-convergence factor. We show that for this family of functions, this convergence factor is superior to the factor obtained from the triple momentum method.

KW - Optimization algorithms

KW - robust control

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U2 - 10.1109/LCSYS.2022.3163408

DO - 10.1109/LCSYS.2022.3163408

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SP - 2449

EP - 2454

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

ER -

Global Convergence and Asymptotic Optimality of the Heavy Ball Method for a Class of Nonconvex Optimization Problems

Abstract

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