Quadratic programming solver that guarantees a boundary point?

I have a problem that I have expressed a开发者_如何学Pythons the minimization of a convex quadratic program with linear constraints. The problem is that I want to disallow any point that is strictly interior (i.e. I only find the answer useful if it is on a vertex of the feasible region.

I'd like to do this without modifying the objective function. I have already considered several modifications that would make this a non-issue, but they all have the unfortunate result of making the program non-convex.

By my estimation my only option for an efficient solution would be a solver that uses a penalty method to approach a solution from the outside of the feasible region. Does anyone know a decent solver for this?

My current objective function is a sum of parabolic cylinders.

Can you just find the vertices of the feasible region and then take the one which minimizes the objective function? This should just involve a bit of linear algebra and then a limited number of evaluations of the objective function.