polyhedra

A combinatorial approach for small and strong formulations of disjunctive constraints

  • Joey Huchette
  • Juan Pablo Vielma
    • Categories (Mixed) Integer Linear Programming Tags , ,

    We present a framework for constructing small, strong mixed-integer formulations for disjunctive constraints. Our approach is a generalization of the logarithmically-sized formulations of Vielma and Nemhauser for SOS2 constraints, and we offer a complete characterization of its expressive power. We apply the framework to a variety of disjunctive constraints, producing novel, small, and strong formulations … Read more

    Orthogonal invariance and identifiability

  • Aris Daniilidis
  • Dmitriy Drusvyatskiy
  • Adrian Lewis
    • Categories Nonsmooth Optimization Tags , , , , ,

    Orthogonally invariant functions of symmetric matrices often inherit properties from their diagonal restrictions: von Neumann’s theorem on matrix norms is an early example. We discuss the example of “identifiability”, a common property of nonsmooth functions associated with the existence of a smooth manifold of approximate critical points. Identifiability (or its synonym, “partial smoothness”) is the … Read more

    Maximizing a Class of Submodular Utility Functions

  • Shabbir Ahmed
  • Alper Atamturk
    • Categories Branch and Cut Algorithms, Integer Programming Tags , , ,

    Given a finite ground set N and a value vector a in R^N, we consider optimization problems involving maximization of a submodular set utility function of the form h(S)= f (sum_{i in S} a_i), S subseteq N, where f is a strictly concave, increasing, differentiable function. This function appears frequently in combinatorial optimization problems when … Read more

    Size constrained graph partitioning polytope. Part I: Dimension and trivial facets

  • Martine Labbé
  • F. Aykut Özsoy
    • Categories 0-1 Programming, Polyhedra Tags , , , , ,

    We consider the problem of clustering a set of items into subsets whose sizes are bounded from above and below. We formulate the problem as a graph partitioning problem and propose an integer programming model for solving it. This formulation generalizes several well-known graph partitioning problems from the literature like the clique partitioning problem, the … Read more