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A distributed algorithm for high-dimension convex quadratically constrained quadratic programs

Author

Listed:
  • Run Chen

    (Purdue University)

  • Andrew L. Liu

    (Purdue University)

Abstract

We propose a Jacobi-style distributed algorithm to solve convex, quadratically constrained quadratic programs (QCQPs), which arise from a broad range of applications. While small to medium-sized convex QCQPs can be solved efficiently by interior-point algorithms, high-dimension problems pose significant challenges to traditional algorithms that are mainly designed to be implemented on a single computing unit. The exploding volume of data (and hence, the problem size), however, may overwhelm any such units. In this paper, we propose a distributed algorithm for general, non-separable, high-dimension convex QCQPs, using a novel idea of predictor–corrector primal–dual update with an adaptive step size. The algorithm enables distributed storage of data as well as parallel, distributed computing. We establish the conditions for the proposed algorithm to converge to a global optimum, and implement our algorithm on a computer cluster with multiple nodes using message passing interface. The numerical experiments are conducted on data sets of various scales from different applications, and the results show that our algorithm exhibits favorable scalability for solving high-dimension problems.

Suggested Citation

  • Run Chen & Andrew L. Liu, 2021. "A distributed algorithm for high-dimension convex quadratically constrained quadratic programs," Computational Optimization and Applications, Springer, vol. 80(3), pages 781-830, December.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:3:d:10.1007_s10589-021-00319-x
    DOI: 10.1007/s10589-021-00319-x
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    References listed on IDEAS

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    1. Brendan O’Donoghue & Eric Chu & Neal Parikh & Stephen Boyd, 2016. "Conic Optimization via Operator Splitting and Homogeneous Self-Dual Embedding," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1042-1068, June.
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