Refining the accuracy of QP interior-point solutions through crossover

[Denis Ridzal]

I'm solving a large QP with very sparse structured constraints using Gurobi's interior-point method.  The methods works very well, outperforming primal and dual simplex by a factor of 100.  The smallest relative solution accuracy I can get is approximately 1e-9, which makes sense for the interior-point solver.  My application requires an accuracy of about 1e-14.  The primal and dual simplex solvers can get near machine precision (1e-16).  How do I perform a crossover from interior-point to simplex solvers for a QP model in Gurobi?  If there is no automated capability, are there other "manual" options?  I've tried providing the interior-point solution as an initial guess for simplex through model.start, but the solver discards it.  I'm using the Matlab interface.

[Robert Luce]

Hello Denis,

unfortunately crossover from QP, or QP simplex warmstart are not supported. You could try to reduce the convergence tolarance of the barrier algorithm a bit, and test whether it improves accuaracy:

http://www.gurobi.com/documentation/8.0/refman/barconvtol.html#parameter:BarConvTol

Setting it too small, however, may have have adverse effects as well. In terms of "manual" options I am not aware of a simple solution.

Robert