On the Distributed Method of Multipliers for Separable Convex Optimization Problems

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Abstract

In this paper, we present a novel method for convex optimization in distributed networks called the distributed method of multipliers (DMM). The proposed method is based on a combination of a particular dual lifting and classic monotone operator splitting approaches to produce an algorithm with guaranteed asymptotic convergence in undirected networks. The proposed method allows any separable convex problem with linear constraints to be solved in undirected networks. In contrast to typical distributed approaches, the structure of the network does not restrict the types of problems that can be solved. Furthermore, the solver can be applied to general separable problems, those with separable convex objectives and constraints, via the use of an additional primal lifting approach. Finally, we demonstrate the use of DMM in solving a number of classic signal processing problems including beamforming, channel capacity maximization and portfolio optimization.
Original languageEnglish
Pages (from-to)495-510
Number of pages16
JournalIEEE Transactions on Signal and Information Processing over Networks
Volume5
Issue number3
DOIs
Publication statusPublished - 2019

Keywords

  • Distributed signal processing
  • convex optimization
  • monotone operator
  • optimization over networks

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