So I'm solving bigger instances of some binary-linear-program using cplex. The formulations of the problem I am using is integer friendly, meaning nearly all of my instances can be solved at the root node. Additionally I have a pretty good heuristic for calculating solutions. The heuristic is quite fast and nearly always gives the globally optimal solution.
When combining cplex with the heuristic I do not achieve the performance gains I expected. I feed the globally optimal solution to cplex as a "warm-start-solution", but it still takes quite some time for cplex to proof its optimality (cplex chooses the dual-simplex for the relaxation).
I might lack some theoretical understanding, but why can't the dual-simplex just build a basis for the supplied optimal solution and show that there is nothing else to do?