ILOG CPLEX 11.0 User's Manual

◆A single QP is solved if both IloCplex.isMIP and IloCplex.isQC return false andIloCplex.isQO returns true. This is the case if the active model contains a quadratic(and positive semi-definite) objective but does not contain:●●●integer variables, Boolean variables, or semi-continuous variables;quadratic terms among the constraints;special ordered sets; or● piecewise linear functions among the constraints.As in the case of LPs, IloCplex provides several optimizing algorithms to solve QPs.For more about identifying this kind of problem, see Solving Problems with aQuadratic Objective (QP) on page 227.◆A single QCP is solved if IloCplex.isMIP returns false and IloCplex.isQCreturns true, indicating that it detected a quadratically constrained program (QCP). Thisis the case if the active model contains one or more quadratic (and positive semi-definite)constraints but does not contain:●●●integer variables, Boolean variables, or semi-continuous variables;special ordered sets; orpiecewise linear functions.IloCplex solves QCP models using the barrier optimizer. For more about this kind ofproblem, see Solving Problems with Quadratic Constraints (QCP) on page 239, wherethe special case of second order cone programming (SOCP) problems is also discussed.In short, an LP model has a linear objective function and linear constraints; a QP model hasa quadratic objective function and linear constraints; a QCP includes quadratic constraints,and it may have a linear or quadratic objective function. A problem that can be representedas LP, QP, or QCP is also known collectively as a continuous model or a continuousrelaxation.A series of relaxations is solved if the active model is a MIP, which can be recognized byIloCplex.isMIP returning true. This is the case if the model contains any of the objectsexcluded for single continuous models. If a MIP contains a purely linear objective function,(that is, IloCplex.isQO returns false), the problem is more precisely called an MILP. Ifit includes a positive semidefinite quadratic term in the objective, it is called an MIQP. If itincludes a constraint that contains a positive semidefinite quadratic term, it is called anMIQCP. MIPs are solved using branch & cut search, explained in more detail in SolvingMixed Integer Programming Problems (MIP) on page 255.Solving a Single Continous ModelTo choose the optimizer to solve a single continous model, or the first continuous relaxationin a series, use84 ILOG CPLEX 11.0 — USER’ S MANUAL