Ambros Gleixner

Three Enhancements for Optimization-Based Bound Tightening

  • Timo Berthold
  • Ambros Gleixner
  • Benjamin Müller
  • Stefan Weltge
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Nonlinear Optimization Tags , , , , ,

    Optimization-based bound tightening (OBBT) is one of the most effective procedures to reduce variable domains of nonconvex mixed-integer nonlinear programs (MINLPs). At the same time it is one of the most expensive bound tightening procedures, since it solves auxiliary linear programs (LPs)—up to twice the number of variables many. The main goal of this paper … Read more

    Iterative Refinement for Linear Programming

  • Ambros Gleixner
  • Kati Wolter
  • Daniel E. Steffy
    • Categories Linear Programming Tags , , ,

    We describe an iterative refinement procedure for computing extended precision or exact solutions to linear programming problems (LPs). Arbitrarily precise solutions can be computed by solving a sequence of closely related LPs with limited precision arithmetic. The LPs solved share the same constraint matrix as the original problem instance and are transformed only by modification … Read more