Areesh Mittal

Finding Minimum Volume Circumscribing Ellipsoids Using Generalized Copositive Programming

  • Grani A. Hanasusanto
  • Areesh Mittal
    • Categories Linear, Cone and Semidefinite Programming

    We study the problem of finding the Lowner-John ellipsoid, i.e., an ellipsoid with minimum volume that contains a given convex set. We reformulate the problem as a generalized copositive program, and use that reformulation to derive tractable semidefinite programming approximations for instances where the set is defined by affine and quadratic inequalities. We prove that, … Read more

    Robust Quadratic Programming with Mixed-Integer Uncertainty

  • Can Gokalp
  • Grani A. Hanasusanto
  • Areesh Mittal
    • Categories Linear, Cone and Semidefinite Programming, Quadratic Programming, Robust Optimization Tags , , ,

    We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are amenable to exact copositive programming reformulations of polynomial size. These convex optimization problems are NP-hard but admit a conservative semidefinite programming … Read more