ill–posed problem

ALGORITHM & DOCUMENTATION: MINRES-QLP for Singular Symmetric and Hermitian Linear Equations and Least-Squares Problems

  • Sou-Cheng Choi
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering, Optimization Software and Modeling Systems Tags , , , , , , , , ,

    We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite … 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

    Multiscale Concepts for Moving Horizon Optimization

  • T. Binder
  • L. Blank
  • W. Dahmen
  • W. Marquardt
    • Categories Applications - Science and Engineering Tags , , , , , , , , ,

    In chemical engineering complex dynamic optimization problems formulated on moving horizons have to be solved on-line. In this work, we present a multiscale approach based on wavelets where a hierarchy of successively, adaptively refined problems are constructed.They are solved in the framework of nested iteration as long as the real-time restrictions are fulfilled. To avoid … Read more