ILOG CPLEX 11.0 User's Manual

Difficulties during OptimizationNumeric difficulties can degrade performance of the ILOG CPLEX Barrier Optimizer oreven prevent convergence toward a solution. There are several possible sources of numericdifficulties:◆◆elimination of too many dense columns may cause numeric instability;tight convergence tolerance may aggravate small numeric inconsistencies in a problem;◆ unbounded optimal faces may remain undetected and thus prevent convergence.The following subsections offer guidance about overcoming those difficulties.Numeric Instability Due to Elimination of Too Many Dense ColumnsDetecting and Eliminating Dense Columns on page 210 explains how to change parametersto encourage ILOG CPLEX to detect and eliminate as many dense columns as possible.However, in some problems, if ILOG CPLEX removes too many dense columns, it maycause numeric instability.You can check how many dense columns ILOG CPLEX removes by looking at thepreprocessing statistics at the beginning of the log file. For example, the following log fileshows that CPLEX removed 2249 columns, of which nine were dense.Selected objective sense: MINIMIZESelected objective name: objSelected RHS name: rhsSelected bound name: bndProblem 'XXX.mps' read.Read time = 0.03 sec.Tried aggregator 1 time.LP Presolve eliminated 2200 rows and 2249 columns.Aggregator did 8 substitutions.Reduced LP has 171 rows, 182 columns, and 1077 nonzeros.Presolve time = 0.02 sec.***NOTE: Found 9 dense columns.Number of nonzeros in lower triangle of A*A' = 6071Using Approximate Minimum Degree orderingTotal time for automatic ordering = 0.00 sec.Summary statistics for Cholesky factor:Rows in Factor = 180Integer space required = 313Total non-zeros in factor = 7286Total FP ops to factor = 416448If you observe that the removal of too many dense columns results in numeric instability inyour problem, then increase the column nonzeros parameter, BarColNz.The default value of the column nonzeros parameter is 0 (zero); that value tellsILOG CPLEX to calculate the parameter automatically.214 ILOG CPLEX 11.0 — USER’ S MANUAL