Yuzhou Qiu

Polyhedral Properties of RLT Relaxations of Nonconvex Quadratic Programs and Their Implications on Exact Relaxations

  • Yuzhou Qiu
  • E. Alper Yildirim
    • Categories Global Optimization, Linear Programming, Quadratic Programming Tags , , ,

    We study linear programming relaxations of nonconvex quadratic programs given by the reformulation-linearization technique (RLT), referred to as RLT relaxations. We investigate the relations between the polyhedral properties of the feasible regions of a quadratic program and its RLT relaxation. We establish various connections between recession directions, boundedness, and vertices of the two feasible regions. … Read more

    On Exact and Inexact RLT and SDP-RLT Relaxations of Quadratic Programs with Box Constraints

  • Yuzhou Qiu
  • E. Alper Yildirim
    • Categories Bound-constrained Optimization, Global Optimization, Quadratic Programming Tags , , ,

    Quadratic programs with box constraints involve minimizing a possibly nonconvex quadratic function subject to lower and upper bounds on each variable. This is a well-known NP-hard problem that frequently arises in various applications. We focus on two convex relaxations, namely the RLT (Reformulation-Linearization Technique) relaxation and the SDP-RLT relaxation obtained by adding semidefinite constraints to … Read more