NDLI: Hybrid Random/Deterministic Parallel Algorithms for Convex and Nonconvex Big Data Optimization

Content Provider	IEEE Xplore Digital Library
Author	Daneshmand, A. Facchinei, F. Kungurtsev, V. Scutari, G.
Copyright Year	1991
Abstract	We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a nonsmooth (possibly nonseparable), convex one. The latter term is usually employed to enforce structure in the solution, typically sparsity. The main contribution of this work is a novel parallel, hybrid random/deterministic decomposition scheme wherein, at each iteration, a subset of (block) variables is updated at the same time by minimizing a convex surrogate of the original nonconvex function. To tackle huge-scale problems, the (block) variables to be updated are chosen according to a mixed random and deterministic procedure, which captures the advantages of both pure deterministic and random update-based schemes. Almost sure convergence of the proposed scheme is established. Numerical results show that on huge-scale problems the proposed hybrid random/deterministic algorithm compares favorably to random and deterministic schemes on both convex and nonconvex problems.
Sponsorship	IEEE Signal Processing Society
Starting Page	3914
Ending Page	3929
Page Count	16
File Size	4292178
File Format	PDF
ISSN	1053587X
Volume Number	63
Issue Number	15
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Convergence Optimization Signal processing algorithms Big data Parallel algorithms Indexes Image processing sparse solution Jacobi method nonconvex problems parallel and distributed methods random selections
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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