Infeasible Solution Information
An important feature of ILOG CPLEX is that even if no feasible solution has been found, that is if cplex.solve() returns false, some information about the problem can be queried when solving LPs or QPs. All the methods discussed so far may successfully return information about the current (infeasible) solution ILOG CPLEX maintains.
Unfortunately, there is no simple comprehensive rule about whether or not current solution information can be queried. This is because by default, ILOG CPLEX uses a presolve procedure to simplify the model. If, for example, the model is proven to be infeasible during the presolve, no current solution is generated by the optimizer. If, in contrast, infeasibility is only proven by the optimizer, current solution information is available to be queried. The status returned by calling cplex.getCplexStatus() may help to determine which case you are facing, but it is probably safer and easier to include the methods for querying the solution within try / catch statements.
Method IloCplex.isPrimalFeasible() can be called to find out if a primal feasible solution has been found and can be queried. Similarly, method IloCplex.isDualFeasible() can be called to find out if a dual feasible solution has been found and can be queried.
When an LP has been proven to be infeasible, ILOG CPLEX provides assistance for determining the cause of the infeasibility. This is done by computing what is known as an irreducibly inconsistent set (IIS), which is a description of the minimal subproblem that is still infeasible. An infeasible subproblem is minimal if, when you remove any of the constraints (including finite bounds), the infeasibility vanishes.
An IIS is computed for an infeasible model by calling method cplex.getIIS(). Currently this method requires that the infeasibility was proven by the primal simplex method. It returns an object of type IloCplex.IIS, which can then be queried to find out what variables and constraints of the infeasible active model take part in the IIS.
