mixed integer convex optimization

Shapes and recession cones in mixed-integer convex representability

  • Miles Lubin
  • Juan Pablo Vielma
  • Ilias Zadik
    • Categories (Mixed) Integer Nonlinear Programming Tags ,

    Mixed-integer convex representable (MICP-R) sets are those sets that can be represented exactly through a mixed-integer convex programming formulation. Following up on recent work by Lubin et al. (2017, 2020) we investigate structural geometric properties of MICP-R sets, which strongly differentiate them from the class of mixed-integer linear representable sets (MILP-R). First, we provide an … Read more

    Disjoint Bilinear Optimization: A Two-Stage Robust Optimization Perspective

  • Danique de Moor
  • Dick den Hertog
  • Ahmadreza Marandi
  • Lieven Vandenberghe
  • Jianzhe Zhen
    • Categories Robust Optimization Tags , , ,

    In this paper, we focus on a subclass of quadratic optimization problems, that is, disjoint bilinear optimization problems. We first show that disjoint bilinear optimization problems can be cast as two-stage robust linear optimization problems with fixed-recourse and right-hand-side uncertainty, which enables us to apply robust optimization techniques to solve the resulting problems. To this … Read more