Benchmarking ADMM in Nonconvex NLPs

Journal Article · 26 August 2018 · Computers and Chemical Engineering

DOI:https://doi.org/10.1016/j.compchemeng.2018.08.036· OSTI ID:1472254

Rodriguez, Jose S. ^[1]; Nicholson, Bethany ^[2]; Laird, Carl ^[2]; Zavala, Victor M. ^[3]

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1. Purdue Univ., West Lafayette, IN (United States). Chemical Engineering
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computer Research
3. Univ. of Wisconsin, Madison, WI (United States). Dept. of Chemical and Biological Engineering

Here, we study connections between the alternating direction method of multipliers (ADMM), the classical method of multipliers (MM), and progressive hedging (PH). The connections are used to derive benchmark metrics and strategies to monitor and accelerate convergence and to help explain why ADMM and PH are capable of solving complex nonconvex NLPs. Specifically, we observe that ADMM is an inexact version of MM and approaches its performance when multiple coordination steps are performed. In addition, we use the observation that PH is a specialization of ADMM and borrow Lyapunov function and primal-dual feasibility metrics used in ADMM to explain why PH is capable of solving nonconvex NLPs. This analysis also highlights that specialized PH schemes can be derived to tackle a wider range of stochastic programs and even other problem classes. Our exposition is tutorial in nature and seeks to to motivate algorithmic improvements and new decomposition strategies.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE Office of Fossil Energy (FE); USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000; NA0003525; SC0014114
• OSTI ID: 1472254
• Report Number(s): SAND--2018-9574J; {"Journal ID: ISSN 0098-1354",667498}
• Journal Information: Computers and Chemical Engineering, Journal Name: Computers and Chemical Engineering Vol. 119; ISSN 0098-1354
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

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decomposition
augmented Lagrangian
ADMM
NLP
large-scale
coordination