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

Journal Article · Thu Nov 28 00:00:00 EST 2019 · Journal of Parallel and Distributed Computing

DOI:https://doi.org/10.1016/j.jpdc.2018.10.009· OSTI ID:1562383

Petra, Cosmin G. ^[1]

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

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.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE; USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 1562383
• Alternate ID(s): OSTI ID: 1636866
• Report Number(s): LLNL-JRNL--739001; 892535
• Journal Information: Journal of Parallel and Distributed Computing, Journal Name: Journal of Parallel and Distributed Computing Journal Issue: C Vol. 133; ISSN 0743-7315
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Parallel interior-point
Parallel optimization
Quasi-Newton