NDLI: Incremental Stochastic Subgradient Algorithms for Convex Optimization

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Veeravalli, V. V. Ram, S. Sundhar Nedi, A.
Copyright Year	2009
Abstract	This paper studies the effect of stochastic errors on two constrained incremental subgradient algorithms. The incremental subgradient algorithms are viewed as decentralized network optimization algorithms as applied to minimize a sum of functions, when each component function is known only to a particular agent of a distributed network. First, the standard cyclic incremental subgradient algorithm is studied. In this, the agents form a ring structure and pass the iterate in a cycle. When there are stochastic errors in the subgradient evaluations, sufficient conditions on the moments of the stochastic errors are obtained that guarantee almost sure convergence when a diminishing step-size is used. In addition, almost sure bounds on the algorithm's performance with a constant step-size are also obtained. Next, the Markov randomized incremental subgradient method is studied. This is a noncyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time nonhomogeneous Markov chain. Such a model is appropriate for mobile networks, as the network topology changes across time in these networks. Convergence results and error bounds for the Markov randomized method in the presence of stochastic errors for diminishing and constant step-sizes are obtained.
Starting Page	691
Ending Page	717
Page Count	27
File Format	PDF
ISSN	10526234
DOI	10.1137/080726380
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	2
Volume Number	20
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2009-06-10
Access Restriction	Subscribed
Subject Keyword	random networks subgradient convex optimization network optimization stochastic approximation incremental optimization Convex programming Distributed algorithms
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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