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Approximate projection methods for decentralized optimization with functional constraints

Publication ,  Journal Article
Lee, S; Zavlanos, MM
Published in: IEEE Transactions on Automatic Control
October 1, 2018

We consider distributed convex optimization problems that involve a separable objective function and nontrivial functional constraints, such as linear matrix inequalities. We propose a decentralized and computationally inexpensive algorithm, which is based on the concept of approximate projections. Our algorithm is one of the consensus-based methods in that, at every iteration, each agent performs a consensus update of its decision variables followed by an optimization step of its local objective function and local constraints. Unlike other methods, the last step of our method is not a Euclidean projection onto the feasible set, but instead a subgradient step in the direction that minimizes the local constraint violation. We propose two different averaging schemes to mitigate the disagreements among the agents' local estimates. We show that the algorithms converge almost surely, i.e., every agent agrees on the same optimal solution, under the assumption that the objective functions and constraint functions are nondifferentiable and their subgradients are bounded. We provide simulation results on a decentralized optimal gossip averaging problem, which involves semidefinite programming constraints, to complement our theoretical results.

Duke Scholars

Published In

IEEE Transactions on Automatic Control

DOI

EISSN

1558-2523

ISSN

0018-9286

Publication Date

October 1, 2018

Volume

63

Issue

10

Start / End Page

3248 / 3260

Related Subject Headings

  • Industrial Engineering & Automation
  • 4007 Control engineering, mechatronics and robotics
  • 0913 Mechanical Engineering
  • 0906 Electrical and Electronic Engineering
  • 0102 Applied Mathematics
 

Citation

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Lee, S., & Zavlanos, M. M. (2018). Approximate projection methods for decentralized optimization with functional constraints. IEEE Transactions on Automatic Control, 63(10), 3248–3260. https://doi.org/10.1109/TAC.2017.2778696
Lee, S., and M. M. Zavlanos. “Approximate projection methods for decentralized optimization with functional constraints.” IEEE Transactions on Automatic Control 63, no. 10 (October 1, 2018): 3248–60. https://doi.org/10.1109/TAC.2017.2778696.
Lee S, Zavlanos MM. Approximate projection methods for decentralized optimization with functional constraints. IEEE Transactions on Automatic Control. 2018 Oct 1;63(10):3248–60.
Lee, S., and M. M. Zavlanos. “Approximate projection methods for decentralized optimization with functional constraints.” IEEE Transactions on Automatic Control, vol. 63, no. 10, Oct. 2018, pp. 3248–60. Scopus, doi:10.1109/TAC.2017.2778696.
Lee S, Zavlanos MM. Approximate projection methods for decentralized optimization with functional constraints. IEEE Transactions on Automatic Control. 2018 Oct 1;63(10):3248–3260.

Published In

IEEE Transactions on Automatic Control

DOI

EISSN

1558-2523

ISSN

0018-9286

Publication Date

October 1, 2018

Volume

63

Issue

10

Start / End Page

3248 / 3260

Related Subject Headings

  • Industrial Engineering & Automation
  • 4007 Control engineering, mechatronics and robotics
  • 0913 Mechanical Engineering
  • 0906 Electrical and Electronic Engineering
  • 0102 Applied Mathematics