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Adaptive Penalty-Based Distributed Stochastic Convex Optimization
- Publication Year :
- 2013
-
Abstract
- In this work, we study the task of distributed optimization over a network of learners in which each learner possesses a convex cost function, a set of affine equality constraints, and a set of convex inequality constraints. We propose a fully-distributed adaptive diffusion algorithm based on penalty methods that allows the network to cooperatively optimize the global cost function, which is defined as the sum of the individual costs over the network, subject to all constraints. We show that when small constant step-sizes are employed, the expected distance between the optimal solution vector and that obtained at each node in the network can be made arbitrarily small. Two distinguishing features of the proposed solution relative to other related approaches is that the developed strategy does not require the use of projections and is able to adapt to and track drifts in the location of the minimizer due to changes in the constraints or in the aggregate cost itself. The proposed strategy is also able to cope with changing network topology, is robust to network disruptions, and does not require global information or rely on central processors.<br />13 pages, 1 figure
- Subjects :
- FOS: Computer and information sciences
Mathematical optimization
Proper convex function
Linear matrix inequality
Network topology
Nonlinear programming
Computer Science - Distributed, Parallel, and Cluster Computing
Optimization and Control (math.OC)
Signal Processing
Convex optimization
FOS: Mathematics
Penalty method
Computer Science - Multiagent Systems
Distributed, Parallel, and Cluster Computing (cs.DC)
Electrical and Electronic Engineering
Drift plus penalty
Mathematics - Optimization and Control
Conic optimization
Mathematics
Multiagent Systems (cs.MA)
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....164982b9c48602513b43f566d751956b