NDLI: Distributed subgradient methods for saddle-point problems

Content Provider	IEEE Xplore Digital Library
Author	Mateos-Nunez, David Cortes, Jorge
Copyright Year	2015
Description	Author affiliation: Univ. of California, San Diego, United States of America (Cortes, Jorge) \|\| UC San Diego, United States of America (Mateos-Nunez, David)
Abstract	We present provably correct distributed subgradient methods for general min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include separable constrained minimization problems where each constraint is a sum of convex functions of local variables for the agents. The proposed algorithm then reduces to primal-dual updates using local subgradients and Laplacian averaging on local copies of the multipliers associated to the global constraints. The framework also encodes minimization problems with semidefinite constraints, which results in novel distributed strategies that are scalable if the order of the matrix inequalities is independent of the network size. Our analysis establishes for the case of general convex-concave functions the convergence of the running time-averages of the local estimates to a saddle point under periodic connectivity of the communication digraphs. Specifically, choosing the gradient step-sizes in a suitable way, we show that the evaluation error is proportional to 1/√t where t is the iteration step.
Starting Page	5462
Ending Page	5467
File Size	381544
Page Count	6
File Format	PDF
e-ISBN	9781479978861
DOI	10.1109/CDC.2015.7403075
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-12-15
Publisher Place	Japan
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Optimization Convergence Convex functions Symmetric matrices Laplace equations Minimization Linear matrix inequalities
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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