slack matrix

Approximate cone factorizations and lifts of polytopes

  • João Gouveia
  • Pablo A. Parrilo
  • Rekha R. Thomas
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    In this paper we show how to construct inner and outer convex approximations of a polytope from an approximate cone factorization of its slack matrix. This provides a robust generalization of the famous result of Yannakakis that polyhedral lifts of a polytope are controlled by (exact) nonnegative factorizations of its slack matrix. Our approximations behave … Read more

    Lifts of Convex Sets and Cone Factorizations

  • João Gouveia
  • Pablo A. Parrilo
  • Rekha R. Thomas
    • Categories Convex Optimization, Semi-definite Programming Tags , , , ,

    In this paper we address the basic geometric question of when a given convex set is the image under a linear map of an affine slice of a given closed convex cone. Such a representation or ‘lift’ of the convex set is especially useful if the cone admits an efficient algorithm for linear optimization over … Read more