ILOG CPLEX 11.0 User's Manual

Ordering-Algorithm Time in the Log FileAfter the number of nonzeros in the lower triangle of AA T , ILOG CPLEX records the timerequired by the ordering algorithm. (The ILOG CPLEX Barrier Optimizer offers you achoice of several ordering algorithms, explained in Choosing an Ordering Algorithm onpage 210.) This section in the log file indicates which ordering algorithm the defaultAutomatic setting chose.Cholesky Factor in the Log FileAfter the time required by the ordering algorithm, ILOG CPLEX records information aboutthe Cholesky factor. ILOG CPLEX computes this matrix on each iteration. The number ofrows in the Cholesky factor represents the number after preprocessing. The next line ofinformation about the Cholesky factor—integer space required—indicates the amount ofmemory needed to store the sparsity pattern of the factored matrix. If this number is low,then the factor can be computed more quickly than when the number is high.Information about the Cholesky factor continues with the number of nonzeros in the factoredmatrix. The difference between this number and the number of nonzeros in AA T indicatesthe fill-level of the Cholesky factor.The final line of information indicates how many floating-point operations are required tocompute the Cholesky factor. This number is the best predictor of the relative time that willbe required to perform each iteration of the barrier optimizer.Iteration Progress in the Log FileAfter the information about the Cholesky factor, the log file records progress at eachiteration. It records both primal and dual objectives (as Primal Obj and Dual Obj) periteration.It also records absolute infeasibilities per iteration. Internally, the ILOG CPLEX BarrierOptimizer treats inequality constraints as equality constraints with added slack and surplusvariables. Consequently, primal constraints in a problem are written as Ax=b and x +s=u,and the dual constraints are written as A T y+z-w=c. As a result, in the log file, theinfeasibilities represent norms, as summarized in Table 10.5.Table 10.5Infeasibilities and Norms in the Log File of a Barrier OptimizationInfeasibility In log file Normprimal Prim Inf |b - Ax|upper Upper Inf |u - (x + s)|dual Dual Inf |c - yA -z+w|204 ILOG CPLEX 11.0 — USER’ S MANUAL