Hey Micah,
This is definitely possible, provided your quadratic constraints are convex 
or second-order cone representable. See this section 
<https://github.com/JuliaOpt/Gurobi.jl#quadratic-programming-examples> of 
the readme for how to set up a QP, and this section 
<https://github.com/JuliaOpt/Gurobi.jl#mixed-integer-programming> for how 
to specify integer variables. Also check out our modeling package JuMP 
<https://github.com/JuliaOpt/JuMP.jl> for an algebraic modeling language 
that I’d recommend using over the lower-level Gurobi interface directly.

Also, there’s a julia-opt mailing list 
<https://groups.google.com/forum/#!forum/julia-opt> we’ve set up for these 
types of questions related to optimization in Julia.

On Saturday, January 17, 2015 at 6:19:59 PM UTC-5, Micah McClimans wrote:

I'm trying to figure out how to set up a Mixed Integer Quadratic Program in 
> Gurobi through Julia, and I'm not seeing how to do it. I'm not seeing 
> anything in the source code that even suggests that it can be done, but 
> since I can't see anything in the Gurobi docs explaining how to do it 
> either, I could very well be missing something important. I'd like to avoid 
> actually modifying the Gurobi package, since I could easily screw something 
> up, but if MIQP can't be done in Gurobi/Julia, I suppose I would.
>
​

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