The optional primal-dual ILOG CPLEX Barrier Optimizer requires a special license. It offers an approach completely different from the primal and dual simplex optimizers and from the network optimizer-an approach particularly efficient in large, sparse problems (for example, more than 1000 rows or columns, relatively few nonzeros per column). Solving LP Problems with the Barrier Optimizer explains this optimizer in greater detail in the context of linear programming, and Chapter 7, Solving Quadratic Programming Problems covers this optimizer in the context of convex quadratic objective functions.