Mustafa Kilinc

Intersection Cuts for Nonlinear Integer Programming: Convexification Techniques for Structured Sets

  • Mustafa Kilinc
  • Sina Modaresi
  • Juan Pablo Vielma
    • Categories (Mixed) Integer Nonlinear Programming

    We study the generalization of split, k-branch split, and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference between a convex set and an open set with a simple geometric structure. We introduce two techniques to give precise … Read more

    Strong Branching Inequalities for Convex Mixed Integer Nonlinear Programs

  • Mustafa Kilinc
  • Jeff Linderoth
  • James R. Luedtke
  • Andrew J. Miller
    • Categories (Mixed) Integer Nonlinear Programming

    Strong branching is an effective branching technique that can significantly reduce the size of the branch-and-bound tree for solving Mixed Integer Nonlinear Programming (MINLP) problems. The focus of this paper is to demonstrate how to effectively use discarded information from strong branching to strengthen relaxations of MINLP problems. Valid inequalities such as branching-based linearizations, various … Read more