SDP-based Branch-and-Bound for Non-convex Quadratic Integer Optimization

Semidefinite programming (SDP) relaxations have been intensively used for solving discrete quadratic optimization problems, in particular in the binary case. For the general non-convex integer case with box constraints, the branch-and-bound algorithm Q-MIST has been proposed [11], which is based on an extension of the well-known SDP-relaxation for max-cut. For solving the resulting SDPs, Q-MIST … Read more

An Exact Algorithm for Quadratic Integer Minimization using Ellipsoidal Relaxations

We propose a branch-and-bound algorithm for minimizing a not necessarily convex quadratic function over integer variables. The algorithm is based on lower bounds computed as continuous minima of the objective function over appropriate ellipsoids. In the nonconvex case, we use ellipsoids enclosing the feasible region of the problem. In spite of the nonconvexity, these minima … Read more

Two-Stage Quadratic Integer Programs with Stochastic Right-Hand Sides

We consider two-stage quadratic integer programs with stochastic right-hand sides, and present an equivalent reformulation using value functions. We fi rst derive some basic properties of value functions of quadratic integer programs. We then propose a two-phase solution approach. The first phase constructs the value functions of quadratic integer programs in both stages. The second phase … Read more