Extended formulations in mixed integer conic quadratic programming

In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Through an homogenization procedure we generalize an existing extended formulation to general conic quadratic constraints. We then compare its effectiveness against traditional and extended formulation-based algorithms for MICQP. We find that this new extended formulation can be used to improve various LP-based algorithms. In particular, the formulation provides an easy-to-implement procedure that, in our benchmarks, significantly improved the performance of commercial MICQP solvers.