Carl D. Laird

An implicit function formulation for optimization of discretized index-1 differential algebraic systems

  • Robert Parker
  • Bethany Nicholson
  • John D. Siirola
  • Carl D. Laird
  • Lorenz T. Biegler
    • Categories Systems governed by Differential Equations Optimization Tags , , ,

    A formulation for the optimization of index-1 differential algebraic equation systems (DAEs) that uses implicit functions to remove algebraic variables and equations from the optimization problem is described. The formulation uses the implicit function theorem to calculate derivatives of functions that remain in the optimization problem in terms of a reduced space of variables, allowing … Read more

    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

    Scalable Preconditioning of Block-Structured Linear Algebra Systems using ADMM

  • Carl D. Laird
  • Victor M. Zavala
  • Jose Rodriguez
    • Categories Parallel Algorithms, Quadratic Programming, Stochastic Programming

    We study the solution of block-structured linear algebra systems arising in optimization by using iterative solution techniques. These systems are the core computational bottleneck of many problems of interest such as parameter estimation, optimal control, network optimization, and stochastic programming. Our approach uses a Krylov solver (GMRES) that is preconditioned with an alternating method of … 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

    Global Solution Strategies for the Network-Constrained Unit Commitment Problem With AC Transmission Constraints

  • Anya Castillo
  • Carl D. Laird
  • Jean-Paul Watson
  • Jianfeng Liu
    • Categories Global Optimization, Integer Programming, Nonlinear Optimization Tags , ,

    We propose a novel global solution algorithm for the network-constrained unit commitment problem that incorporates a nonlinear alternating current model of the transmission network, which is a nonconvex mixed-integer nonlinear programming (MINLP) problem. Our algorithm is based on the multi-tree global optimization methodology, which iterates between a mixed-integer lower-bounding problem and a nonlinear upper-bounding problem. … Read more

    Nonlinear Programming Strategies on High-Performance Computers

  • Naiyuan Chiang
  • Carl D. Laird
  • Victor M. Zavala
  • Jia Kang
    • Categories Constrained Nonlinear Optimization, Parallel Algorithms, Systems governed by Differential Equations Optimization

    We discuss structured nonlinear programming problems arising in control applications, and we review software and hardware capabilities that enable the efficient exploitation of such structures. We focus on linear algebra parallelization strategies and discuss how these interact and influence high-level algorithmic design elements required to enforce global convergence and deal with negative curvature in a … Read more

    Clustering-Based Preconditioning for Stochastic Programs

  • Yankai Cao
  • Carl D. Laird
  • Victor M. Zavala
    • Categories Linear Programming, Quadratic Programming, Stochastic Programming

    We present a clustering-based preconditioning strategy for KKT systems arising in stochastic programming within an interior-point framework. The key idea is to perform adaptive clustering of scenarios (inside-the-solver) based on their influence on the problem as opposed to cluster scenarios based on problem data alone, as is done in existing (outside-thesolver) approaches. We derive spectral … Read more

    A Fast Moving Horizon Estimation Algorithm Based on Nonlinear Programming Sensitivity

  • Lorenz T. Biegler
  • Carl D. Laird
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    Moving Horizon Estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the attractiveness of this method, its application in industrial settings has been rather limited. This has been mainly due to the difficulty to solve, in real-time, the associated dynamic optimization problems. In this work, a fast MHE algorithm able to overcome this … Read more

    An algorithmic framework for convex mixed integer nonlinear programs

  • Lorenz T. Biegler
  • Pierre Bonami
  • Andrew R. Conn
  • Gérard Cornuéjols
  • Ignacio E. Grossmann
  • Carl D. Laird
  • Jon Lee
  • Andrea Lodi
  • François Margot
  • Nicolas Sawaya
    • Categories (Mixed) Integer Nonlinear Programming

    This paper is motivated by the fact that mixed integer nonlinear programming is an important and difficult area for which there is a need for developing new methods and software for solving large-scale problems. Moreover, both fundamental building blocks, namely mixed integer linear programming and nonlinear programming, have seen considerable and steady progress in recent … Read more