s-free sets

On a generalization of the Chvatal-Gomory closure

  • Sanjeeb Dash
  • Oktay Gunluk
  • Dabeen Lee
    • Categories Cutting Plane Approaches, Integer Programming Tags , , , , ,

    Many practical integer programming problems involve variables with one or two-sided bounds. Dunkel and Schulz (2012) considered a strengthened version of Chvatal-Gomory (CG) inequalities that use 0-1 bounds on variables, and showed that the set of points in a rational polytope that satisfy all these strengthened inequalities is a polytope. Recently, we generalized this result … Read more

    Outer-Product-Free Sets for Polynomial Optimization and Oracle-Based Cuts

  • Daniel Bienstock
  • Chen Chen
  • Gonzalo Muñoz
    • Categories Constrained Nonlinear Optimization, Cutting Plane Approaches, Global Optimization Theory Tags , ,

    Cutting planes are derived from specific problem structures, such as a single linear constraint from an integer program. This paper introduces cuts that involve minimal structural assumptions, enabling the generation of strong polyhedral relaxations for a broad class of problems. We consider valid inequalities for the set $S\cap P$, where $S$ is a closed set, … Read more