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Scalable Parallel Nonlinear Optimization with PyNumero and Parapint

Author

Listed:
  • Jose S. Rodriguez

    (Davidson School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907)

  • Robert B. Parker

    (Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123; Carnegie Mellon University, Department of Chemical Engineering, Pittsburgh, Pennsylvania 15213)

  • Carl D. Laird

    (Carnegie Mellon University, Department of Chemical Engineering, Pittsburgh, Pennsylvania 15213)

  • Bethany L. Nicholson

    (Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123)

  • John D. Siirola

    (Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123)

  • Michael L. Bynum

    (Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123)

Abstract

We describe PyNumero, an open-source, object-oriented programming framework in Python that supports rapid development of performant parallel algorithms for structured nonlinear programming problems (NLP’s) using the Message Passing Interface (MPI). PyNumero provides three fundamental building blocks for developing NLP algorithms: a fast interface for calculating first and second derivatives with the AMPL Solver Library (ASL), a number of interfaces to efficient linear solvers, and block-structured vectors and matrices based on NumPy, SciPy, and MPI that support distributed parallel storage and computation. PyNumero’s design enables efficient, parallel algorithm development using high-level Python syntax while keeping expensive numerical calculations in fast, compiled implementations based on languages like C and Fortran. To demonstrate the utility of PyNumero, we also present Parapint, a Python package built on PyNumero for parallel solution of dynamic optimization problems. Parapint includes a parallel interior-point solver based on Schur-Complement decomposition. We illustrate the effectiveness of PyNumero for developing parallel algorithms with both code examples and scalability analyses for parallel matrix-vector dot products, parallel solution of structured systems of linear equations using Schur-Complement decomposition, and the parallel solution of a two-dimensional PDE optimal control problem. Our numerical results show nearly perfect scaling to more than 1,000 cores for large matrix-vector dot products and structured linear systems. Moreover, we obtain more than 354 times speedup for the optimal control example.

Suggested Citation

  • Jose S. Rodriguez & Robert B. Parker & Carl D. Laird & Bethany L. Nicholson & John D. Siirola & Michael L. Bynum, 2023. "Scalable Parallel Nonlinear Optimization with PyNumero and Parapint," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 509-517, March.
    • Handle: RePEc:inm:orijoc:v:35:y:2023:i:2:p:509-517
    DOI: 10.1287/ijoc.2023.1272
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    References listed on IDEAS

    as
    1. Daniel Word & Jia Kang & Johan Akesson & Carl Laird, 2014. "Efficient parallel solution of large-scale nonlinear dynamic optimization problems," Computational Optimization and Applications, Springer, vol. 59(3), pages 667-688, December.
    2. Charles R. Harris & K. Jarrod Millman & Stéfan J. Walt & Ralf Gommers & Pauli Virtanen & David Cournapeau & Eric Wieser & Julian Taylor & Sebastian Berg & Nathaniel J. Smith & Robert Kern & Matti Picu, 2020. "Array programming with NumPy," Nature, Nature, vol. 585(7825), pages 357-362, September.
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