GMRES-Accelerated ADMM for Quadratic Objectives
Name
16m1059941.pdf
Description
Published version
Size
1.09 MB
Format
Adobe PDF
Checksum (MD5)
1f61f7ee139461b42043928e11946237
Author(s)
Zhang, Richard Y
White, Jacob K
Date Issued
2018
Journal
SIAM Journal on Optimization
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
© 2018 Society for Industrial and Applied Mathematics. We consider the sequence acceleration problem for the alternating direction method of multipliers (ADMM) applied to a class of equality-constrained problems with strongly convex quadratic objectives, which frequently arise as the Newton subproblem of interior-point methods. Within this context, the ADMM update equations are linear, the iterates are confined within a Krylov subspace, and the general minimum residual (GMRES) algorithm is optimal in its ability to accelerate convergence. The basic ADMM method solves a Κ -conditioned problem in O(√Κ) iterations. We give theoretical justification and numerical evidence that the GMRES-accelerated variant consistently solves the same problem in O(Κ 1 / 4 ) iterations for an order-of-magnitude reduction in iterations, despite a worst-case bound of O(√Κ) iterations. The method is shown to be competitive against standard preconditioned Krylov subspace methods for saddle-point problems. The method is embedded within SeDuMi, a popular open-source solver for conic optimization written in MATLAB, and used to solve many large-scale semidefinite programs with error that decreases like O(1/k 2 ), instead of O(1/k), where k is the iteration index.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
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Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/16M1059941
