I'm using IBM's CPLEX (or ILOG) quadratic programming solver through it's cplexqp function in matlab and getting a weird behavior where when the problem is feasible it is quick to succeed (e.g. 5-10 seconds) but when it is not feasible is fails very slowly (60-300 seconds). The problem is quite large, e.g. 3000-10000 inequality constraints, on N=100-500 variables.
The exit flag there is 5 meaning 'Solution with numerical issues'. Changing the tolerance from 1e-3 to 1e-10 (through options.simplex.tolerances.feasibility and options.simplex.tolerances.optimality) didn't remove this asymmetry.
I'm guessing it tries "too hard" to avoid the numerical issues. Any suggestions for relevant parameters?
