A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs

@article{Linderoth2005ASB,
  title={A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs},
  author={Jeff T. Linderoth},
  journal={Math. Program.},
  year={2005},
  volume={103},
  pages={251-282}
}
We propose a branch-and-bound algorithm for solving nonconvex quadratically-constrained quadratic programs. The algorithm is novel in that branching is done by partitioning the feasible region into the Cartesian product of two-dimensional triangles and rectangles. Explicit formulae for the convex and concave envelopes of bilinear functions over triangles and rectangles are derived and shown to be second-order cone representable. The usefulness of these new relaxations is demonstrated both… CONTINUE READING