We have described how the ILOG CPLEX Barrier Optimizer finds primal and dual solutions from the primal and dual formulations of a model (see the section Identifying LPs for Barrier Optimization) , but you do not have to reformulate the problem yourself. The ILOG CPLEX Barrier Optimizer automatically creates the primal and dual formulations of the problem for you after you enter or read in the problem.

In the Interactive Optimizer, we recommend this way of working with the ILOG CPLEX Barrier Optimizer:

Enter the problem. You enter an LP problem to solve with the barrier optimizer just as you enter other LP problems. In the Interactive Optimizer, use the enter command to type in the problem data interactively, or use the read command to read a problem from a file in MPS, LP, or SAV format.
Check the number of nonzeros in the Cholesky factor. To do so, use the command set barrier limits iterations 0; then use the command baropt stop. These two commands together will make ILOG CPLEX count the number of nonzeros in the Cholesky factor but stop before it begins barrier iterations.
Check for dense columns. If you use the command display problem histogram c, ILOG CPLEX will show you the number of columns with nonzeros in the unpreprocessed problem. If you want to see the density of columns in the processed, presolved, aggregated problem, do this:

a. Write the preprocessed problem to a file with the file extension .pre; use the write command to do so.

b. Read the file in with the read command.

c. Display the histogram with its column option: display problem histogram c. You will be able to identify dense columns at a glance.

Use the baropt command to start optimization.

The option stop tells ILOG CPLEX to stop with a nonbasis barrier solution. (Afterwards, you can apply the command primopt or tranopt explicitly to this nonbasis, barrier solution to cross over to a primal or dual basic solution.)

The option primopt (or the shortcut p) tells ILOG CPLEX to cross over automatically to a basic solution using the primal simplex optimizer.

The option dualopt (or the shortcut d) tells ILOG CPLEX to cross over to a basic solution using the dual simplex optimizer.

If you specify no option, ILOG CPLEX assumes dualopt.

Check ILOG CPLEX progress. Use the command set barrier display to change the level of information displayed on the screen or logged to a file.

Initialize the ILOG CPLEX environment, create the problem object, and populate the problem object, as explained in Creating an Application with CPLEX Concert Technology Library and Using the Callable Library in an Application.

• In the Concert Technology Library, use the method:

  • cplex.setRootAlgorithm(IloCplex::Barrier) to invoke the CPLEX Barrier Optimizer without crossover.

  • cplex.setRootAlgorithm(IloCplex::BarrierPrimal) to invoke the CPLEX Barrier Optimizer with primal crossover.

  • cplex.setRootAlgorithm(IloCplex::BarrierDual) to invoke the CPLEX Barrier Optimizer with dual crossover.

• In the Callable Library, use the routine:

  • CPXhybbaropt() to invoke the ILOG CPLEX Barrier Optimizer with crossover.

  • CPXbaropt() to invoke the ILOG CPLEX Barrier Optimizer without crossover.