convex integer programming

Quadratic Outer Approximation for Convex Integer Programming

  • Christoph Buchheim
  • Long Trieu
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Quadratic Programming Tags , ,

    We present a quadratic outer approximation scheme for solving general convex integer programs, where suitable quadratic approximations are used to underestimate the objective function instead of classical linear approximations. As a resulting surrogate problem we consider the problem of minimizing a function given as the maximum of finitely many convex quadratic functions having the same … Read more

    Some Properties of Convex Hulls of Integer Points Contained in General Convex Sets

  • Santanu S. Dey
  • Diego Moran Ramirez
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    In this paper, we study properties of general closed convex sets that determine the closed-ness and polyhedrality of the convex hull of integer points contained in it. We first present necessary and sufficient conditions for the convex hull of integer points contained in a general convex set to be closed. This leads to useful results … Read more