lift-and-project relaxations

Copositive and Semidefinite Relaxations of the Quadratic Assignment Problem

  • Janez Povh
  • Franz Rendl
    • Categories 0-1 Programming, Combinatorial Optimization, Semi-definite Programming Tags , , ,

    Semidefinite relaxations of the quadratic assignment problem (QAP) have recently turned out to provide good approximations to the optimal value of QAP. We take a systematic look at various conic relaxations of QAP. We first show that QAP can equivalently be formulated as a linear program over the cone of completely positive matrices. Since it … Read more

    Semidefinite-Based Branch-and-Bound for Nonconvex Quadratic Programming

  • Samuel Burer
  • Dieter Vandenbussche
    • Categories Global Optimization, Quadratic Programming, Semi-definite Programming Tags , , , ,

    This paper presents a branch-and-bound algorithm for nonconvex quadratic programming, which is based on solving semidefinite relaxations at each node of the enumeration tree. The method is motivated by a recent branch-and-cut approach for the box-constrained case that employs linear relaxations of the first-order KKT conditions. We discuss certain limitations of linear relaxations when handling … Read more