A. Mahajan, S. Leyffer, C. Kirches, "Solving Mixed-Integer Nonlinear Programs by QP-Diving," Preprint ANL/MCS-P2071-0312, March 2012. [pdf]
We present a new tree-search algorithm for solving mixed-integer nonlinear programs (MINLPs). Rather than relying on computationally expensive nonlinear solves at every node of the branch-and-bound tree, our algorithm solves a quadratic approximation at every node. We show that the resulting algorithm retains global convergence properties for convex MINLPs, and we present numerical results on a range of test problems. Our numerical experience shows that the new algorithm allows us to exploit warm-starting techniques from quadratic programming,resulting in a reduction in solve times for convex MINLPs by orders of magnitude on some classes of problems.