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Title: Benchmarking ADMM in Nonconvex NLPs

Abstract

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.

Authors:
 [1]; ORCiD logo [2];  [2];  [3]
  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
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Fossil Energy (FE); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1472254
Report Number(s):
SAND-2018-9574J
Journal ID: ISSN 0098-1354; 667498
Grant/Contract Number:  
AC04-94AL85000; NA0003525; SC0014114
Resource Type:
Accepted Manuscript
Journal Name:
Computers and Chemical Engineering
Additional Journal Information:
Journal Volume: 119; Journal ID: ISSN 0098-1354
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; decomposition; augmented Lagrangian; ADMM; NLP; large-scale; coordination

Citation Formats

Rodriguez, Jose S., Nicholson, Bethany, Laird, Carl, and Zavala, Victor M. Benchmarking ADMM in Nonconvex NLPs. United States: N. p., 2018. Web. doi:10.1016/j.compchemeng.2018.08.036.
Rodriguez, Jose S., Nicholson, Bethany, Laird, Carl, & Zavala, Victor M. Benchmarking ADMM in Nonconvex NLPs. United States. doi:10.1016/j.compchemeng.2018.08.036.
Rodriguez, Jose S., Nicholson, Bethany, Laird, Carl, and Zavala, Victor M. Mon . "Benchmarking ADMM in Nonconvex NLPs". United States. doi:10.1016/j.compchemeng.2018.08.036. https://www.osti.gov/servlets/purl/1472254.
@article{osti_1472254,
title = {Benchmarking ADMM in Nonconvex NLPs},
author = {Rodriguez, Jose S. and Nicholson, Bethany and Laird, Carl and Zavala, Victor M.},
abstractNote = {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.},
doi = {10.1016/j.compchemeng.2018.08.036},
journal = {Computers and Chemical Engineering},
number = ,
volume = 119,
place = {United States},
year = {2018},
month = {8}
}

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