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Title: A memory-distributed quasi-Newton solver for nonlinear programming problems with a small number of general constraints

Abstract

We approach the problem of parallelizing state-of-the-art nonlinear programming optimization algorithms.Specifically, we focus on parallelizing quasi-Newton interior-point methods that use limited-memory secant Hessian approximations. Such interior-point methods are known to have better convergence properties and to be more effective on large-scale problems than gradient-based and derivative-free 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 “reduced-space” optimization approach. We introduce and analyze the time and space complexity of a decomposition method for solving the quasi-Newton linear systems that leverages the fact that the quasi-Newton Hessian matrix has a small number of dense blocks that border a low-rank update of a diagonal matrix. This enables an efficient parallelization on memory-distributed computers of the iterations of the optimization algorithm, a state-of-the-art filter line-search interior-point 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 » machine.« less

Authors:
ORCiD logo [1]
  1. 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):
LLNL-JRNL-739001
Journal ID: ISSN 0743-7315; 892535
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Parallel and Distributed Computing
Additional Journal Information:
Journal Volume: 133; Journal Issue: C; Journal ID: ISSN 0743-7315
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Parallel optimization; Parallel interior-point; Quasi-Newton

Citation Formats

Petra, Cosmin G. A memory-distributed quasi-Newton 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 memory-distributed quasi-Newton 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 memory-distributed quasi-Newton 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 memory-distributed quasi-Newton solver for nonlinear programming problems with a small number of general constraints},
author = {Petra, Cosmin G.},
abstractNote = {We approach the problem of parallelizing state-of-the-art nonlinear programming optimization algorithms.Specifically, we focus on parallelizing quasi-Newton interior-point methods that use limited-memory secant Hessian approximations. Such interior-point methods are known to have better convergence properties and to be more effective on large-scale problems than gradient-based and derivative-free 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 “reduced-space” optimization approach. We introduce and analyze the time and space complexity of a decomposition method for solving the quasi-Newton linear systems that leverages the fact that the quasi-Newton Hessian matrix has a small number of dense blocks that border a low-rank update of a diagonal matrix. This enables an efficient parallelization on memory-distributed computers of the iterations of the optimization algorithm, a state-of-the-art filter line-search interior-point 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},
number = C,
volume = 133,
place = {United States},
year = {2019},
month = {11}
}

Journal Article:
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This content will become publicly available on November 28, 2020
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