miqcp

A MIQCP formulation for B-spline constraints

  • Bjarne Grimstad
    • Categories (Mixed) Integer Nonlinear Programming, Basic Sciences Applications Tags , , , ,

    This paper presents a mixed-integer quadratically constrained programming (MIQCP) formulation for B-spline constraints. The formulation can be used to obtain an exact MIQCP reformulation of any spline-constrained optimization problem, provided that the polynomial spline functions are continuous. This reformulation allows practitioners to use a general-purpose MIQCP solver, instead of a special-purpose spline solver, when solving … Read more

    Convex Relaxations of Non-Convex Mixed Integer Quadratically Constrained Programs: Extended Formulations

  • Pierre Bonami
  • Jon Lee
  • Anureet Saxena
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Tags , ,

    This paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non-convexities: integer variables and non-convex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the lift-and-project methodology. In particular, … Read more