On exploiting structure induced when modelling an intersection of cones in conic optimization

Conic optimization is the problem of optimizing a linear function over an intersection of an affine linear manifold with the Cartesian product of convex cones. However, many real world conic models involves an intersection rather than the product of two or more cones. It is easy to deal with an intersection of one or more cones but unfortunately it leads to an expansion in the optimization problem size and hence to an increase in the computational complexity of solving the optimization problem. In this note we discuss how to handle the intersection of two or more cones. In particular we show that the important special case of the intersection of a linear and a quadratic cone can be handled in a computational efficient way.