symbolic computation

From Computational Certification to Exact Coordinates: Heilbronn’s Triangle Problem on the Unit Square Using Mixed-Integer Optimization

  • Nathan Sudermann-Merx
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Integer Programming Tags , , , ,

    We develop a mixed-integer nonlinear programming (MINLP) approach for the classical Heilbronn triangle problem, demonstrating the capability of modern global optimization solvers to tackle challenging combinatorial geometry problems. A symmetry-breaking strategy based on boundary structure yields a substantially stronger model: for n=9, we compute an epsilon-globally optimal point in 15 minutes on a standard desktop … Read more

    Linear Programming using Limited-Precision Oracles

  • Ambros Gleixner
  • Daniel E. Steffy
    • Categories Linear Programming, Optimization Software and Modeling Systems Tags , , , , , , ,

    Since the elimination algorithm of Fourier and Motzkin, many different methods have been developed for solving linear programs. When analyzing the time complexity of LP algorithms, it is typically either assumed that calculations are performed exactly and bounds are derived on the number of elementary arithmetic operations necessary, or the cost of all arithmetic operations … Read more