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.
And then you call the solution routine just as for any other ILOG CPLEX optimizer.