Michael Lee Bynum

Scalable Parallel Nonlinear Optimization with PyNumero and Parapint

  • Jose Rodriguez
  • Robert Parker
  • Carl D. Laird
  • Bethany Nicholson
  • John D. Siirola
  • Michael Lee Bynum
    • Categories Nonlinear Optimization, Parallel Algorithms Tags ,

    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), … Read more

    Decomposing Optimization-Based Bounds Tightening Problems Via Graph Partitioning

  • Michael Lee Bynum
  • Anya Castillo
  • Bernard Knueven
  • Carl D. Laird
  • Jean-Paul Watson
  • John D. Siirola
    • Categories Global Optimization

    Bounds tightening or domain reduction is a critical refinement technique used in global optimization algorithms for nonlinear and mixed-integer nonlinear programming problems. Bounds tightening can strengthen convex relaxations and reduce the size of branch and bounds trees. An effective but computationally intensive bounds tightening technique is optimization-based bounds tightening (OBBT). In OBBT, each variable is … Read more

    GALINI: An extensible mixed-integer quadratically-constrained optimization solver

  • Radu Baltean-Lugojan
  • Michael Lee Bynum
  • Francesco Ceccon
  • Chun Li
  • Ruth Misener
    • Categories Optimization Software Design Principles

    We present GALINI, an open source solver for nonconvex mixed-integer quadratically-constrained quadratic programs formulated with the Python algebraic modeling library Pyomo. GALINI uses Pyomo to represent optimization problems and leverages the existing library ecosystem to implement different parts of the solver. GALINI includes a generic branch \& bound algorithm that can be use develop new … Read more

    Tightening McCormick Relaxations Toward Global Solution of the ACOPF Problem

  • Michael Lee Bynum
  • Anya Castillo
  • Carl D. Laird
  • Jean-Paul Watson
    • Categories Global Optimization Applications Tags , ,

    We show that a strong upper bound on the objective of the alternating current optimal power flow (ACOPF) problem can significantly improve the effectiveness of optimization-based bounds tightening (OBBT) on a number of relaxations. We additionally compare the performance of relaxations of the ACOPF problem, including the rectangular form without reference bus constraints, the rectangular … Read more