Michael A. Saunders

MadNCL: A GPU Implementation of Algorithm NCL for Large-Scale, Degenerate Nonlinear Programs

  • François Pacaud
  • Alexis Montoison
  • Dominique Orban
  • Sungho Shin
  • Michael A. Saunders
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization

    We present a GPU implementation of Algorithm NCL, an augmented Lagrangian method for solving large-scale and degenerate nonlinear programs. Although interior-point methods and sequential quadratic programming are widely used for solving nonlinear programs, the augmented Lagrangian method is known to offer superior robustness against constraint degeneracies and can rapidly detect infeasibility. We introduce several enhancements … Read more

    On the Performance of SQP Methods for Nonlinear Optimization

  • Philip E. Gill
  • Michael A. Saunders
  • Elizabeth Wong
    • Categories Constrained Nonlinear Optimization, Optimization Software Benchmark Tags , , ,

    This paper concerns some practical issues associated with the formulation of sequential quadratic programming (SQP) methods for large-scale nonlinear optimization. SQP methods find an approximate solution of a sequence of quadratic programming (QP) subproblems in which a quadratic model of the objective function is minimized subject to the linearized constraints. Extensive numerical results are given … Read more

    MINRES-QLP: a Krylov subspace method for indefinite or singular symmetric systems

  • Sou-Cheng Choi
  • Christopher Paige
  • Michael A. Saunders
    • Categories Convex Optimization, Optimization Software and Modeling Systems, Statistics Tags , , , , , , ,

    CG, SYMMLQ, and MINRES are Krylov subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and SYMMLQ’s solution could explode, while MINRES would give a least-squares solution but not necessarily the minimum-length (pseudoinverse) solution. This … Read more

    A globally convergent linearly constrained Lagrangian method for nonlinear optimization

  • Michael P. Friedlander
  • Michael A. Saunders
    • Categories Constrained Nonlinear Optimization Tags , ,

    For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form “minimize an augmented Lagrangian function subject to linearized constraints”. Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. The well known software package MINOS has proven effective on many … Read more