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I am trying to solve a QP problem.

Does anybody know the differences between the interior-point-convex algorithm of quadprog and the barrier method of Gurobi in terms which kind of matrices can the solvers handle the best? Sparse matrices or dense matrices? And what kind of problems: large problems or small problems? Furthermore, which solver needs more iterations (with less expensive cost per iteration) and which solver needs fewer iterations, but expensive cost/time per iteration.

From results, I think Gurobi gives more iterations and quadprog less, but I do not know why?

And what are the differences with GPAD by means of what is described above?

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