A memorydistributed quasiNewton solver for nonlinear programming problems with a small number of general constraints
Abstract
We approach the problem of parallelizing stateoftheart nonlinear programming optimization algorithms.Specifically, we focus on parallelizing quasiNewton interiorpoint methods that use limitedmemory secant Hessian approximations. Such interiorpoint methods are known to have better convergence properties and to be more effective on largescale problems than gradientbased and derivativefree optimization algorithms. We target nonlinear and potentially nonconvex optimization problems with an arbitrary number of bound constraints and a small number of general equality and inequality constraints on the optimization variables. These problems occur for example in the form of optimal control, optimal design, and inverse problems governed by ordinary or partial differential equations, whenever they are expressed in a “reducedspace” optimization approach. We introduce and analyze the time and space complexity of a decomposition method for solving the quasiNewton linear systems that leverages the fact that the quasiNewton Hessian matrix has a small number of dense blocks that border a lowrank update of a diagonal matrix. This enables an efficient parallelization on memorydistributed computers of the iterations of the optimization algorithm, a stateoftheart filter linesearch interiorpoint algorithm by Wächter et. al. We illustrate the efficiency of the proposed method by solving structural topology optimization problems on up to 4608 cores on a parallelmore »
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1562383
 Report Number(s):
 LLNLJRNL739001
Journal ID: ISSN 07437315; 892535
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of Parallel and Distributed Computing
 Additional Journal Information:
 Journal Volume: 133; Journal Issue: C; Journal ID: ISSN 07437315
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Parallel optimization; Parallel interiorpoint; QuasiNewton
Citation Formats
Petra, Cosmin G. A memorydistributed quasiNewton solver for nonlinear programming problems with a small number of general constraints. United States: N. p., 2019.
Web. doi:10.1016/j.jpdc.2018.10.009.
Petra, Cosmin G. A memorydistributed quasiNewton solver for nonlinear programming problems with a small number of general constraints. United States. doi:10.1016/j.jpdc.2018.10.009.
Petra, Cosmin G. Thu .
"A memorydistributed quasiNewton solver for nonlinear programming problems with a small number of general constraints". United States. doi:10.1016/j.jpdc.2018.10.009.
@article{osti_1562383,
title = {A memorydistributed quasiNewton solver for nonlinear programming problems with a small number of general constraints},
author = {Petra, Cosmin G.},
abstractNote = {We approach the problem of parallelizing stateoftheart nonlinear programming optimization algorithms.Specifically, we focus on parallelizing quasiNewton interiorpoint methods that use limitedmemory secant Hessian approximations. Such interiorpoint methods are known to have better convergence properties and to be more effective on largescale problems than gradientbased and derivativefree optimization algorithms. We target nonlinear and potentially nonconvex optimization problems with an arbitrary number of bound constraints and a small number of general equality and inequality constraints on the optimization variables. These problems occur for example in the form of optimal control, optimal design, and inverse problems governed by ordinary or partial differential equations, whenever they are expressed in a “reducedspace” optimization approach. We introduce and analyze the time and space complexity of a decomposition method for solving the quasiNewton linear systems that leverages the fact that the quasiNewton Hessian matrix has a small number of dense blocks that border a lowrank update of a diagonal matrix. This enables an efficient parallelization on memorydistributed computers of the iterations of the optimization algorithm, a stateoftheart filter linesearch interiorpoint algorithm by Wächter et. al. We illustrate the efficiency of the proposed method by solving structural topology optimization problems on up to 4608 cores on a parallel machine.},
doi = {10.1016/j.jpdc.2018.10.009},
journal = {Journal of Parallel and Distributed Computing},
issn = {07437315},
number = C,
volume = 133,
place = {United States},
year = {2019},
month = {11}
}