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Global Convergence of the Heavy-ball Method for Convex Optimization
KTH, School of Electrical Engineering (EES), Automatic Control.
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0003-1149-4715
KTH, School of Electrical Engineering (EES), Automatic Control.
2015 (English)In: European Control Conference (ECC15), IEEE , 2015Conference paper, Published paper (Refereed)
Abstract [en]

This paper establishes global convergence and provides global bounds of the rate of convergence for the Heavy-ball method for convex optimization. When the objective function has Lipschitz-continuous gradient, we show that the Cesáro average of the iterates converges to the optimum at a rate of O(1/k) where k is the number of iterations. When the objective function is also strongly convex, we prove that the Heavy-ball iterates converge linearly to the unique optimum. Numerical examples validate our theoretical findings.

Place, publisher, year, edition, pages
IEEE , 2015.
Keyword [en]
Optimization, Convex, Heavy ball, Gradient iteration
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-183460DOI: 10.1109/ECC.2015.7330562Scopus ID: 2-s2.0-84963894675OAI: oai:DiVA.org:kth-183460DiVA: diva2:911488
Conference
ECC 2015
Note

QC 20160314

Available from: 2016-03-12 Created: 2016-03-12 Last updated: 2016-03-14Bibliographically approved

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Ghadimi, EuhannaFeyzmahdavian, Hamid RezaJohansson, Mikael
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CiteExportLink to record
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Citation style
  • apa
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