ILOG CPLEX 11.0 User's Manual

To see the current value of the column nonzeros parameter (either one you have set or oneILOG CPLEX has automatically calculated) you need to look at the level two display, bysetting the BarDisplay parameter to 2.If you decide that the current value of the column nonzeros parameter is inappropriate foryour problem and thus tells ILOG CPLEX to remove too many dense columns, then you canincrease the parameter BarColNz to keep the number of dense columns removed low.Small Numeric Inconsistencies and Tight Convergence ToleranceIf your problem contains small numeric inconsistencies, it may be difficult for theILOG CPLEX Barrier Optimizer to achieve a satisfactory solution at the default setting ofthe complementarity convergence tolerance. In such a case, you should increase theconvergence tolerance parameter (BarEpComp for LP or QP models, BarQCPEpComp forQCP models).Unbounded Variables and Unbounded Optimal FacesAn unbounded optimal face occurs in a model that contains a sequence of optimal solutions,all with the same value for the objective function and unbounded variable values. TheILOG CPLEX Barrier Optimizer will fail to terminate normally if an undetected unboundedoptimal face exists.Normally, the ILOG CPLEX Barrier Optimizer uses its barrier growth parameter,BarGrowth, to detect such conditions. If this parameter is increased beyond its defaultvalue, the ILOG CPLEX Barrier Optimizer will be less likely to detect that the problem hasan unbounded optimal face and more likely to encounter numeric difficulties.Consequently, you should change the barrier growth parameter only if you find that theILOG CPLEX Barrier Optimizer is terminating its work before it finds the true optimumbecause it has falsely detected an unbounded face.Difficulties with Unbounded ProblemsILOG CPLEX detects unbounded problems in either of two ways:◆ either it finds a solution with small complementarity that is not feasible for either theprimal or the dual formulation of the problem;◆ or the iterations tend toward infinity with the objective value becoming very large inabsolute value.The ILOG CPLEX Barrier Optimizer stops when the absolute value of either the primal ordual objective exceeds the objective range parameter, BarObjRng.If you increase the value of BarObjRng, then the ILOG CPLEX Barrier Optimizer williterate more times before it decides that the current problem suffers from an unboundedobjective value.If you know that your problem has large objective values, consider increasing BarObjRng.ILOG CPLEX 11.0 — USER’ S MANUAL 215