CVXGEN only addresses LPs and convex QPs. So I am guessing you are interested in convex Mixed Integer QPs (MIQPs), or perhaps MILPs. Those are addressed, by among others, GUROBI, CPLEX, and MOSEK, all of which also handle the more general Mixed Integer Second Order Cone Problems (MISOCPs).
Once you get into the mixed integer realm, all bets are off regarding the execution time. Convex MIQPs can be vastly more challenging to solve quickly than convex QPs, but it depends on the particular problem. There is also the matter of whether the solvers are available on your processor/OS. There may be other solvers, and various non-default options, which are faster for your particular problems.
If you google
you will see many links, some of which point to specialized software for particular problems.