ILOG CPLEX 11.0 User's Manual

smaller in absolute value than the optimality tolerance, then solving the problem with asmaller optimality tolerance may result in an improvement in the objective function.To change the optimality tolerance, set the parameter for optimality tolerance ( EpOpt inConcert Technology, CPX_PARAM_EPOPT in the Callable Library).Maximum Row ResidualThe maximum row residual identifies the maximum constraint violation. ILOG CPLEXSimplex optimizers control these residuals only indirectly by applying numerically soundmethods to solve the given linear system. When ILOG CPLEX terminates with an infeasiblesolution, all infeasibilities will appear as bound violations on structural or slack variables,not constraint violations. The maximum row residual may help you decide whether a modelof your problem is poorly scaled, or whether the final basis (whether it is optimal orinfeasible) is ill-conditioned.Maximum Dual ResidualThe maximum dual residual indicates the numeric accuracy of the reduced costs in thecurrent solution. By construction, in exact arithmetic, the dual residual of a basic solution isalways 0 (zero). A nonzero value is thus the effect of roundoff error due to finite-precisionarithmetic in the computation of the dual solution vector. Thus, a significant nonzero valueindicates ill conditioning.Maximum Absolute Values: Detecting Ill-Conditioned ProblemsWhen you are trying to decide whether your problem is ill-conditioned, you also need toconsider the following maximum absolute values, all available in the infeasibility analysisthat ILOG CPLEX provides you:◆◆◆variables;slack variables;dual variables;◆ reduced costs (that is, dual slack variables).When using the Component Libraries, use the method cplex.getQuality or the routineCPXgetdblquality to access the information provided by the commanddisplay solution quality in the Interactive Optimizer.If you discover from this analysis that your model is indeed ill-conditioned, then you need toreformulate it. Coping with an Ill-Conditioned Problem or Handling Unscaled Infeasibilitieson page 190 outlines steps to follow in this situation.Finding a ConflictIf ILOG CPLEX reports that your problem is infeasible, then you can invoke tools ofILOG CPLEX to help you analyze the source of the infeasibility. These diagnostic toolsILOG CPLEX 11.0 — USER’ S MANUAL 193