# MIQP: How does Pavito treat convex quadratic functions?

Some Integer Programming solvers, e.g. CPLEX, provide specialised algorithms for convex quadratic constraints and objectives. Does Pavito enable such algorithms for a quadratic objective, or is it treated as a general nonlinear function?

Pavito is for Convex-MINLP, Pajarito is specialized to Convex-MIConicP. If your problem has a QP structure, Pajarito might be the better solver.

Thanks! I have integer problems with linear and convex nonlinear constraints and a convex quadratic objective. Perhaps some combination of Pavito and Pajarito could be best?

Having now studied Pavito’s algorithm.jl in more detail, I understand that quadratics are treated as any nonlinear functions. This could be forgoing some speed. Indeed, using a linear objective produced 50 - 200x speed-ups for different instances, other things being equal. Probably some of these gains could be possible with a quadratic objective if, say, a native MIQP in CPLEX were used.

Got it. This sounds like a good feature to add to Pavito. I would recommend opening an issue in that repo.

Good idea. I guess a quad objective shouldn’t be too hard to add.

If you’re interested in performance, consider writing your convex constraints in conic form. Doing so allows the solver to take advantage of extended formulations and is often more reliable (our paper). I don’t know enough about your use case to say whether it’s a clear win or not, however.

The analogue of your question in Pajarito is addressed by the soc_in_mip option that enables passing second-order cone constraints to the MIP solver instead of outer-approximating them.

I’ve had a look at the paper. It is very interesting, and the approach seems quite promising. I’ll look into applying it. Thank you!