convex hull

Finite Disjunctive Programming Characterizations for General Mixed-Integer Linear Programs

  • Binyuan Chen
  • Simge Küçükyavuz
  • Suvrajeet Sen
    • Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches Tags , , ,

    In this paper, we give a finite disjunctive programming procedure to obtain the convex hull of general mixed-integer linear programs (MILP) with bounded integer variables. We propose a finitely convergent convex hull tree algorithm which constructs a linear program that has the same optimal solution as the associated MILP. In addition, we combine the standard … Read more

    Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and Sets

  • J. William Helton
  • Jiawang Nie
    • Categories Semi-definite Programming Tags , , , , , , , , , , , ,

    The article proves sufficient conditions and necessary conditions for SDP representability of convex sets and convex hulls by proposing a new approach to construct SDP representations. The contributions of this paper are: (i) For bounded SDP representable sets $W_1,\cdots,W_m$, we give an explicit construction of an SDP representation for $conv(\cup_{k=1}^mW_k)$. This provides a technique for … Read more