Mixed-integer nonlinear optimization

Mixed-Integer Programming Techniques for the Minimum Sum-of-Squares Clustering Problem

  • Jan Pablo Burgard
  • Carina Moreira Costa
  • Christopher Hojny
  • Kleinert Thomas
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Data-Mining Tags , , ,

    The minimum sum-of-squares clustering problem is a very important problem in data mining and machine learning with very many applications in, e.g., medicine or social sciences. However, it is known to be NP-hard in all relevant cases and to be notoriously hard to be solved to global optimality in practice. In this paper, we develop … Read more

    Compact extended formulations for low-rank functions with indicator variables

  • Shaoning Han
  • Andrés Gómez
    • Categories (Mixed) Integer Nonlinear Programming Tags , , ,

    We study the mixed-integer epigraph of a special class of convex functions with non-convex indicator constraints, which are often used to impose logical constraints on the support of the solutions. The class of functions we consider are defined as compositions of low-dimensional nonlinear functions with affine functions Extended formulations describing the convex hull of such … Read more