Hongbo Dong

Separation and Relaxation for cones of quadratic forms

  • Samuel Burer
  • Hongbo Dong
    • Categories Global Optimization Theory, Linear, Cone and Semidefinite Programming, Quadratic Programming Tags , , , , ,

    Let P be a pointed, polyhedral cone in R_n. In this paper, we study the cone C = cone{xx^T: x \in P} of quadratic forms. Understanding the structure of C is important for globally solving NP-hard quadratic programs over P. We establish key characteristics of C and construct a separation algorithm for C provided one … Read more

    Separating Doubly Nonnegative and Completely Positive Matrices

  • Kurt M. Anstreicher
  • Hongbo Dong
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization Theory, Linear, Cone and Semidefinite Programming Tags , ,

    The cone of Completely Positive (CP) matrices can be used to exactly formulate a variety of NP-Hard optimization problems. A tractable relaxation for CP matrices is provided by the cone of Doubly Nonnegative (DNN) matrices; that is, matrices that are both positive semidefinite and componentwise nonnegative. A natural problem in the optimization setting is then … Read more