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On the Convergence of an Alternating Direction Penalty Method for Nonconvex Problems
KTH, School of Electrical Engineering (EES), Automatic Control.
KTH, School of Electrical Engineering (EES), Automatic Control.
McGill University, Department of Electrical and Computer Engineering.
KTH, School of Electrical Engineering (EES), Automatic Control.ORCID iD: 0000-0001-9810-3478
2015 (English)In: Signals, Systems and Computers, 2015 Asilomar Conference on, IEEE Computer Society, 2015Conference paper (Other academic)
Abstract [en]

This paper investigates convergence properties ofscalable algorithms for nonconvex and structured optimization.We consider a method that is adapted from the classic quadraticpenalty function method, the Alternating Direction PenaltyMethod (ADPM). Unlike the original quadratic penalty functionmethod, in which single-step optimizations are adopted, ADPMuses alternating optimization, which in turn is exploited toenable scalability of the algorithm. A special case of ADPM isa variant of the well known Alternating Direction Method ofMultipliers (ADMM), where the penalty parameter is increasedto infinity. We show that due to the increasing penalty, theADPM asymptotically reaches a primal feasible point undermild conditions. Moreover, we give numerical evidence thatdemonstrates the potential of the ADPM for computing localoptimal points when the penalty is not updated too aggressively.

Place, publisher, year, edition, pages
IEEE Computer Society, 2015.
Keyword [en]
Distributed optimization, non-convex optimization
National Category
Signal Processing
Research subject
Electrical Engineering
URN: urn:nbn:se:kth:diva-157324DOI: 10.1109/ACSSC.2014.7094558ScopusID: 2-s2.0-84940555102OAI: diva2:769621
Forty-Ninth Asilomar Conference on Signals, Systems and Computers,Pacific Grove, California,November 8-11, 2015

QC 20151202

Available from: 2014-12-08 Created: 2014-12-08 Last updated: 2015-12-02Bibliographically approved

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