Scalable Preconditioning of Block-Structured Linear Algebra Systems using ADMM
- Purdue Univ., West Lafayette, IL (United States). Davidson School of Chemical Engineering
- Purdue Univ., West Lafayette, IL (United States). Davidson School of Chemical Engineering; Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Univ. of Wisconsin-Madison, Madison, WI (United States). Dept. of Chemical and Biological Engineering
In this paper, we study the solution of block-structured linear algebra systems arising in optimization by using iterative solution techniques. These systems are the core computational bottleneck of many problems of interest such as parameter estimation, optimal control, network optimization, and stochastic programming. Our approach uses a Krylov solver (GMRES) that is preconditioned with an alternating method of multipliers (ADMM). We show that this ADMM-GMRES approach overcomes well-known scalability issues of Schur complement decomposition in problems that exhibit a high degree of coupling. The effectiveness of the approach is demonstrated using linear systems that arise in stochastic optimal power flow problems and that contain up to 2 million total variables and 4,000 coupling variables. We find that ADMM-GMRES is nearly an order of magnitude faster than Schur complement decomposition. Moreover, we demonstrate that the approach is robust to the selection of the augmented Lagrangian penalty parameter, which is a key advantage over the direct use of ADMM.
- Research Organization:
- Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE Office of Fossil Energy (FE)
- Grant/Contract Number:
- AC04-94AL85000
- OSTI ID:
- 1570258
- Alternate ID(s):
- OSTI ID: 1703344
- Report Number(s):
- SAND--201911128J; 679764
- Journal Information:
- Computers and Chemical Engineering, Journal Name: Computers and Chemical Engineering Journal Issue: C Vol. 133; ISSN 0098-1354
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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