Like the ILOG CPLEX simplex optimizers, the barrier optimizer records information about its progress in a log file as it works. Some users find it helpful to keep a new log file for each session. By default, ILOG CPLEX records information in a file named cplex.log. In the:

Here is an example of a log file for a barrier optimization (without crossover):

Tried aggregator 1 time.
LP Presolve eliminated 9 rows and 11 columns.
Aggregator did 6 substitutions.
Reduced LP has 12 rows, 15 columns, and 38 nonzeros.
Presolve time =    0.00 sec.
Number of nonzeros in lower triangle of A*A' = 26
Using Approximate Minimum Degree ordering
Total time for automatic ordering = 0.00 sec.
Summary statistics for Cholesky factor:
  Rows in Factor            = 12
  Integer space required    = 12
  Total non-zeros in factor = 78
  Total FP ops to factor    = 650
 Itn      Primal Obj        Dual Obj  Prim Inf Upper Inf  Dual Inf          
   0  -1.3177911e+01  -1.2600000e+03  6.55e+02  0.00e+00  3.92e+01
   1  -4.8683118e+01  -5.4058675e+02  3.91e+01  0.00e+00  1.18e+01
   2  -1.6008142e+02  -3.5969226e+02  1.35e-13  7.11e-15  5.81e+00
   3  -3.5186681e+02  -6.1738305e+02  1.59e-10  1.78e-15  5.16e-01
   4  -4.5808732e+02  -4.7450513e+02  5.08e-12  1.95e-14  4.62e-02
   5  -4.6435693e+02  -4.6531819e+02  1.66e-12  1.27e-14  1.59e-03
   6  -4.6473085e+02  -4.6476678e+02  5.53e-11  2.17e-14  2.43e-15
   7  -4.6475237e+02  -4.6475361e+02  5.59e-13  2.99e-14  2.19e-15
   8  -4.6475312e+02  -4.6475316e+02  1.73e-13  1.55e-14  1.17e-15
   9  -4.6475314e+02  -4.6475314e+02  1.45e-13  2.81e-14  2.17e-15

Barrier - Optimal:  Objective =   -4.6475314194e+02
Solution time =    0.01 sec.  Iterations = 9

Preprocessing in the Log File

The opening lines of that log file record information about preprocessing by the ILOG CPLEX presolver and aggregator. After those preprocessing statistics, the next line records the number of nonzeros in the lower triangle of a particular matrix, AAT, denoted A*A' in the log file.

Nonzeros in Lower Triangle of AAT in the Log File

The number of nonzeros in the lower triangle of AA^T gives an early indication of how long each barrier iteration will take. The larger this number, the more time each barrier iteration requires. If this number is close to 50% of the square of the number of rows, then the problem may contain dense columns that are not being detected. In that case, examine the histogram of column counts; then consider setting the barrier column-nonzeros parameter to a value that enables ILOG CPLEX to treat more columns as being dense.

Ordering-Algorithm Time in the Log File

Cholesky Factor in the Log File

After the time required by the ordering algorithm, ILOG CPLEX records information about the Cholesky factor. ILOG CPLEX computes this matrix on each iteration. The number of rows in the Cholesky factor represents the number after preprocessing. The next line of information about the Cholesky factor - integer space required - indicates the amount of memory 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 factored matrix. The difference between this number and the number of nonzeros in AA^T indicates the fill-level of the Cholesky factor.

The final line of information indicates how many floating-point operations are required to compute the Cholesky factor. This number is the best predictor of the time that will be required to perform each iteration of the barrier method.

Iteration Progress in the Log File

After the information about the Cholesky factor, the log file records progress at each iteration. It records both primal and dual objectives (as Primal Obj and Dual Obj) per iteration.

If solution values are large in absolute value, then the infeasibilities may appear inordinately large because they are recorded in the log file in absolute terms. The optimizer uses relative infeasibilities as termination criteria.

Infeasibility Ratio in the Log File

If you are using one of the barrier infeasibility algorithms available in the ILOG CPLEX Barrier Optimizer (that is, if you have set BarAlg to either 1 or 2, as discussed later in this chapter), then ILOG CPLEX records an additional column of output titled Inf Ratio, the infeasibility ratio. This ratio, always positive, is a measure of progress for that particular algorithm. In a problem with an optimal solution, you will see this ratio increase to a large number. In contrast, in a problem that is infeasible or unbounded, this ratio will decrease to a very small number.