Sina Modaresi

Convex hull of two quadratic or a conic quadratic and a quadratic inequality

  • Sina Modaresi
  • Juan Pablo Vielma
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory, Second-Order Cone Programming Tags , ,

    In this paper we consider an aggregation technique introduced by Yildiran, 2009 to study the convex hull of regions defined by two quadratic or by a conic quadratic and a quadratic inequality. Yildiran shows how to characterize the convex hull of open sets defined by two strict quadratic inequalities using Linear Matrix Inequalities (LMI). We … Read more

    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