ILOG CPLEX 11.0 User's Manual > Continuous Optimization > Solving Problems with Quadratic Constraints (QCP) > Identifying a Quadratically Constrained Program (QCP) |
Identifying a Quadratically Constrained Program (QCP) |
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The distinguishing characteristic of QCP is that quadratic terms may appear in one or more constraints of the problem. The objective function of such a problem may or may not contain quadratic terms as well. Thus, the most general formulation of a QCP is:
Minimize 1/2xTQx + cTx
subject to Ax ~ b
and aiTx + xTQix ri for i=1,...,q
with these bounds l x u
As with a quadratic objective function, convexity plays an important role in quadratic constraints. The constraints must each define a convex region. To make sure of convexity, ILOG CPLEX requires that each Qi matrix be positive semi-definite (PSD) or that the constraint must be in the form of a second order cone. The following sections offer more information about these concepts.
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