Evaluation of Direct and Iterative Approaches for the Parallel Solution of Structured Nonlinear Optimization Problems

Large-scale nonlinear optimization problems arise in a variety of applications and often exhibit some structure, which can be exploited by the use of parallel decompositions to speed up the solution. We present a general problem formulation for structured optimization problems and apply the interior...

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Bibliographic Details
Published in:IFAC-PapersOnLine 2024-01, Vol.58 (14), p.793-798
Main Authors: Lueg, Laurens R., Bynum, Michael, Laird, Carl D., Biegler, Lorenz T.
Format: Article
Language:English
Subjects:
distributed optimization for large-scale systems
nonlinear optimization
parallel computing
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Summary:Large-scale nonlinear optimization problems arise in a variety of applications and often exhibit some structure, which can be exploited by the use of parallel decompositions to speed up the solution. We present a general problem formulation for structured optimization problems and apply the interior point method, outlining different approaches to parallelize the step computations using the Schur complement decomposition. The use of an iterative linear solver can boost performance, given an appropriate preconditioner for the Schur complement. We present an approach to use sparse factorizations from previous solver iterations as a preconditioner, and compare it to both an L-BFGS preconditioner and direct solution.
ISSN:2405-8963
2405-8963
DOI:10.1016/j.ifacol.2024.08.434