I did mean to write mixed integer convex optimization; on the other hand, conic programming includes convex programming as a special case (and vice versa in the

I did mean to write mixed integer convex optimization; on the other hand, conic programming includes convex programming as a special case (and vice versa in the case where cones are convex). Most convex problems we solve (e.g. When written in a high level DSL like CVXPY) are reduced to conic forms (such as SOCPs, but also SDPs, etc) before they are solved.