ILOG CPLEX 11.0 User's Manual

RootAlg parameter (QPMETHOD in the Interactive Optimizer and in the Callable Library).Table 12.1 shows you the possible settings.Table 12.1 RootAlg Parameter SettingsRootAlgValueOptimizer0 Automatic (default)1 Primal Simplex2 Dual Simplex3 Network Simplex4 Barrier5 Sifting6 ConcurrentMany of the optimizer tuning decisions for LP apply in the QP case; and parameters thatcontrol Barrier and Simplex optimizers in the LP case can be set for the QP case, although insome instances to differing effect. Most models are solved fastest by default parametersettings. See the LP chapter for tuning advice.Just as for the LP case, each of the available QP optimizers automatically preprocesses yourmodel, conducting presolution problem analysis and reductions appropriate for a QP.The Barrier optimizer for QP supports crossover, but unlike other LP optimizers, itscrossover step is off by default for QPs. The QP Simplex optimizers return basic solutions,and these bases can be used for purposes of restarting sequences of optimizations, forexample. As a result, application writers who wish to allow end users control over the choiceof QP optimizer need to be aware of this fundamental difference and to program carefully.For most purposes, the nonbasic barrier solution is entirely satisfactory, in that all suchsolutions fully satisfy the standard optimality and feasibility conditions of optimizationtheory.Diagnosing QP InfeasibilityDiagnosis of an infeasible QP problem can be carried out by the conflict refiner. SeeDiagnosing Infeasibility by Refining Conflicts on page 391.Note that it is possible for the outcome of that analysis to be a confirmation that your model(viewed as an LP) is feasible after all. This is typically a symptom that your QP model isnumerically unstable, or ill-conditioned. Unlike the simplex optimizers for LP, the QPILOG CPLEX 11.0 — USER’ S MANUAL 235