ADMM Based Methods for Time-Domain Decomposition Formulations of Optimal Control Problems

This thesis investigates alternating direction method of multipliers (ADMM)-based methods for time-domain decomposition (TDD) formulations of linear-quadratic partial differential equation (PDE)-constrained optimization problems. The solution of such optimization problems is computing time and memory intensive. TDD formulations split the time-dependent PDE into coupled subdomain equations and introduce potential for parallelism and global memory reduction. This thesis tailors ADMM to the TDD structure. ADMM requires the parallel solution of smaller subdomain problems and reduces the number of variables that need to be kept in memory globally. Different TDD splittings lead to different ADMM variants. ADMM convergence analyses are derived from a matrix-splitting view and from the equivalence to the Douglas-Rachford algorithm applied to the dual problem, and are applied to these different variants. The effectiveness of ADMM as a preconditioner within GMRES is investigated. Computational results are presented for several variants of ADMM applied to an advection-diffusion problem.

Name thesis:degree_name

Master of Arts

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Engineering

Grantor

Rice University

Year dc:date.issued

2020

Author dc:creator

• Kroeger, Nathaniel James

Advisor dc:contributor.advisor

• Heinkenschloss, Matthias

• Time Domain Decomposition
• Alternating Direction Method of Multipliers
• ADMM

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/109174

OAI identifier oai:identifier

oai:repository.rice.edu:1911/109174