## Extending a CIP framework to solve MIQCPs

• This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP). The advantage of this approach is that we can utilize the full power of advanced MIP and CP technologies. In particular, this addresses the linear relaxation and the discrete components of the problem. For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints. Further, we give an overview of the reformulation, separation, and propagation techniques that are used to handle the quadratic constraints efficiently. We implemented these methods in the branch-cut-and-price framework SCIP. Computational experiments indicates the potential of the approach.

Author: Timo Berthold, Stefan Heinz, Stefan Vigerske Jon Lee, Sven Leyffer In Collection Mixed Integer Nonlinear Programming 154 427 444 The IMA Volumes in Mathematics and its Applications Springer 2012 978-1-4614-1927-3 urn:nbn:de:0297-zib-11371

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