binarization

Enhancements of Discretization Approaches for Non-Convex Mixed-Integer Quadratically Constraint Quadratic Programming: Part II

  • Ben Beach
  • Robert Burlacu
  • Andreas Bärmann
  • Lukas Hager
  • Robert Hildebrand
    • Categories (Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Quadratic Programming Tags , , , ,

    Abstract. This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products and extend the well-known MIP relaxation normalized multiparametric disaggregation technique (NMDT), applying a sophisticated discretization to both … Read more

    Enhancements of Discretization Approaches for Non-Convex Mixed-Integer Quadratically Constraint Quadratic Programming: Part I

  • Ben Beach
  • Robert Burlacu
  • Andreas Bärmann
  • Lukas Hager
  • Robert Hildebrand
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , , , ,

    We study mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non-convex continuous variable products. In Part I, we consider MIP relaxations based on separable reformulation. The main focus is the introduction of the enhanced separable MIP relaxation for non-convex quadratic products … Read more

    Parity Polytopes and Binarization

  • Dominik Ermel
  • Matthias Walter
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Polyhedra Tags , , ,

    We consider generalizations of parity polytopes whose variables, in addition to a parity constraint, satisfy certain ordering constraints. More precisely, the variable domain is partitioned into k contiguous groups, and within each group, we require the variables to be sorted nonincreasingly. Such constraints are used to break symmetry after replacing an integer variable by a … Read more