If the ILOG CPLEX Barrier Optimizer reports that your QP is primal infeasible, then you can ask ILOG CPLEX to relax the QP to its linear version with the Q matrix set to 0.

To change the problem type:

• In the Interactive Optimizer, use the command change problem zeroed_qp.

• From the Callable Library, use the routine CPXchgprobtype()

You can then solve the relaxed linear version by means of a ILOG CPLEX simplex optimizer, such as primal simplex or dual simplex. Then you can apply the ILOG CPLEX infeasibility finder to that relaxed solution, with its associated, original QP information, to help you diagnose the source of the infeasibility. (Diagnosing LP Infeasibility explains how to use the ILOG CPLEX infeasibility finder following a simplex optimizer.)

Since IloCplex handles problem types transparently, the way to diagnose an infeasible model is slightly different. Since infeasibility does not depend on the objective function, you start by removing the objective extractable from the extracted model. This way, the model seen by the cplex object is an LP with a 0 objective and the LP IIS finder can be applied. To get the original model back, simply add the objective back to the model.