quadratic problems

Convex envelopes for quadratic and polynomial functions over polytopes

  • Marco Locatelli
    • Categories Global Optimization Theory Tags , , , ,

    In this paper we consider the problem of computing the value and a supporting hyperplane of the convex envelope for quadratic and polynomial functions over polytopes with known vertex set. We show that for general quadratic functions the computation can be carried on through a copositive problem, but in some cases (including all the two-dimensional … Read more

    On convex envelopes and underestimators for bivariate functions

  • Marco Locatelli
  • Fabio Schoen
    • Categories Global Optimization, Semi-definite Programming Tags , , ,

    In this paper we discuss convex underestimators for bivariate functions. We first present a method for deriving convex envelopes over the simplest two-dimensional polytopes, i.e., triangles. Next, we propose a technique to compute the value at some point of the convex envelope over a general two-dimensional polytope, together with a supporting hyperplane of the convex … Read more