A distributed algorithm for nonconvex quadratically constrained programs

M. E. Ashour, C. M. Lagoa

Research output: Contribution to journalConference articlepeer-review

Abstract

This paper considers nonconvex quadratically constrained programs over undirected connected graphs. We focus on problems whose quadratic constraint forms have sparse hessians, i.e., each constraint only involves a small subset of variables. We present both centralized and distributed treatment of the problem, where the centralized method is used as a benchmark with which we compare the performance of the proposed distributed algorithm. Towards this objective, we derive a lower bound on the optimal value of the problem using a semidefinite relaxation. Then, we develop a decentralized algorithm based on proximal gradient ADMM that exploits the structure of the constraints to distribute the computations among the graph nodes. Indeed, the proposed algorithm does away with a central node. Each node updates its local variables via solving a simple subproblem, then communicate with its immediate neighbors. An application of this work is the AC optimal power flow problem in power networks for which we provide preliminary numerical results to validate our findings.

Original languageEnglish (US)
Pages (from-to)4252-4257
Number of pages6
JournalIFAC-PapersOnLine
Volume53
DOIs
StatePublished - 2020
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: Jul 12 2020Jul 17 2020

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

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