Distributed constrained optimization by consensus-based primal-dual perturbation method

Tsung Hui Chang, Angelia Nedić, Anna Scaglione

Research output: Contribution to journalArticle

166 Scopus citations

Abstract

Various distributed optimization methods have been developed for solving problems which have simple local constraint sets and whose objective function is the sum of local cost functions of distributed agents in a network. Motivated by emerging applications in smart grid and distributed sparse regression, this paper studies distributed optimization methods for solving general problems which have a coupled global cost function and have inequality constraints. We consider a network scenario where each agent has no global knowledge and can access only its local mapping and constraint functions. To solve this problem in a distributed manner, we propose a consensus-based distributed primal-dual perturbation (PDP) algorithm. In the algorithm, agents employ the average consensus technique to estimate the global cost and constraint functions via exchanging messages with neighbors, and meanwhile use a local primal-dual perturbed subgradient method to approach a global optimum. The proposed PDP method not only can handle smooth inequality constraints but also non-smooth constraints such as some sparsity promoting constraints arising in sparse optimization. We prove that the proposed PDP algorithm converges to an optimal primal-dual solution of the original problem, under standard problem and network assumptions. Numerical results illustrating the performance of the proposed algorithm for a distributed demand response control problem in smart grid are also presented.

Original languageEnglish (US)
Article number6748910
Pages (from-to)1524-1538
Number of pages15
JournalIEEE Transactions on Automatic Control
Volume59
Issue number6
DOIs
StatePublished - Jun 2014

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Keywords

  • Average consensus
  • constrained optimization
  • demand side management control
  • distributed optimization
  • primaldual subgradient method
  • regression
  • smart grid

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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