ILOG CPLEX 11.0 User's Manual

To change the off-diagonal quadratic term from 4 to 6, use this sequence of commands in theInteractive Optimizer:CPLEX> change qptermChange which quadratic term ['variable' 'variable']: a bPresent quadratic term of variable 'a', variable 'b' is 4.000000.Change quadratic term of variable 'a', variable 'b' to what: 6.0Quadratic term of variable 'a', variable 'b' changed to 6.000000.From the Callable Library, the CPXchgqpcoef call to change the off-diagonal term from 4to 6 would change both of the off-diagonal matrix coefficients from 2 to 3. Thus, the indiceswould be 0 and 1, and the new matrix coefficient value would be 3.If you have entered a linear problem without any quadratic terms, and you want to createquadratic terms, you must first change the problem type to QP. To do so, use the commandchange problem qp. This command will create an empty quadratic matrix with Q =0.When you change quadratic terms, there are still restrictions on the properties of the Qmatrix. In a minimization problem, it must be convex, positive semi-definite. In amaximization problem, it must be concave, negative semi-definite. For example, if youchange the sense of an objective function in a convex Q matrix from minimization tomaximization, you will thus make the problem unsolvable. Likewise, in a convex Q matrix,if you make a diagonal term negative, you will thus make the problem unsolvable.Optimizing QPsILOG CPLEX allows you to solve your QP models through a simple interface, by calling thedefault optimizer as follows:●●In the Interactive Optimizer, use the command optimize.From the Callable Library, use the routine CPXqpopt.● In Concert applications, use the solve method of IloCplex.With default settings, this will result in the barrier optimizer being called to solve acontinuous QP.For users who wish to tune the performance of their applications, there are two Simplexoptimizers to try for solving QPs. They are Dual Simplex and Primal Simplex. You can alsouse the Network Simplex optimizer; this solves the model as an LP network (temporarilyignoring the quadratic term in the objective function) and takes this solution as a startingpoint for the Primal Simplex QP optimizer. This choice of QP optimizer is controlled by the234 ILOG CPLEX 11.0 — USER’ S MANUAL