ILOG CPLEX 11.0 User's Manual

Normalized errors, for example, represent the accuracy of satisfying the constraints whileconsidering the quantities used to compute Ax on each row and y T A on each column. In theprimal case, for each row, consider the nonzero coefficients and the x j values used tocompute Ax. If these numbers are large in absolute value, then it is acceptable to have alarger absolute error in the primal constraint.Similar reasoning applies to the dual constraint.If ILOG CPLEX returned an optimal solution, but the primal error seems high to you, theprimal normalized error should be low, since it takes into account the scaling of the problemand solution.After a simplex optimization—whether primal, dual, or network—or after a crossover, thedisplay command will display information related to the quality of the simplex solution.Tuning Barrier Optimizer PerformanceNaturally, the default parameter settings for the ILOG CPLEX Barrier Optimizer work beston most problems. However, you can tune several algorithmic parameters to improveperformance or to overcome numeric difficulties.To help you decide whether default settings of parameters are best for your model, orwhether other parameter settings may improve performance, the tuning tool is available.Tuning Tool on page 161 explains more about this utility and shows you examples of its use.The following sections document parameters particularly relevant to performance andnumeric difficulties in the barrier optimizer:◆ Memory Emphasis: Letting the Optimizer Use Disk for Storage on page 208◆ Preprocessing on page 209;◆ Detecting and Eliminating Dense Columns on page 210;◆ Choosing an Ordering Algorithm on page 210;◆ Using a Starting-Point Heuristic on page 211.In addition, several parameters set termination criteria. With them, you control whenILOG CPLEX stops optimization.You can also control convergence tolerance—another factor that influences performance.Convergence tolerance specifies how nearly optimal a solution ILOG CPLEX must find:tight convergence tolerance means ILOG CPLEX must keep working until it finds a solutionvery close to the optimal one; loose tolerance means ILOG CPLEX can return a solutionwithin a greater range of the optimal one and thus stop calculating sooner.Performance of the ILOG CPLEX Barrier Optimizer is most highly dependent on thenumber of floating-point operations required to compute the Cholesky factor at eachILOG CPLEX 11.0 — USER’ S MANUAL 207