conic optimization problems

Strong duality of a conic optimization problem with a single hyperplane and two cone constraints

  • Sunyoung Kim
  • Masakazu Kojima
    • Categories Convex Optimization, Global Optimization Theory, Linear, Cone and Semidefinite Programming Tags , , , ,

    Strong (Lagrangian) duality of general conic optimization problems (COPs) has long been studied and its profound and complicated results appear in different forms in a wide range of literatures. As a result, characterizing the known and unknown results can sometimes be difficult. The aim of this article is to provide a unified and geometric view … Read more

    A Geometrical Analysis of a Class of Nonconvex Conic Programs for Convex Conic Reformulations of Quadratic and Polynomial Optimization Problems

  • Sunyoung Kim
  • Masakazu Kojima
  • Kim-Chuan Toh
    • Categories Linear, Cone and Semidefinite Programming Tags , , ,

    We present a geometrical analysis on the completely positive programming reformulation of quadratic optimization problems and its extension to polynomial optimization problems with a class of geometrically defined nonconvex conic programs and their covexification. The class of nonconvex conic programs is described with a linear objective function in a linear space $V$, and the constraint … Read more