ILOG CPLEX 11.0 User's Manual

You can also use the network optimizer when solving QPs (that is, problems with a positivesemi-definite quadratic term in the objective function), but not when solving quadraticallyconstrained problems. To do so using the Callable Library, you set the parameterCPX_PARAM_QPMETHOD to CPX_ALG_NET. For Concert Technology, the RootAlg parametermust be set to Network. When ILOG CPLEX uses the network optimizer to solve a QP, itfirst ignores the quadratic term and uses the network optimizer to solve the resulting LP.ILOG CPLEX then uses the resulting basis to start a simplex algorithm on the QP modelwith the original quadratic objective.Network ExtractionThe ILOG CPLEX network extractor searches an LP constraint matrix for a submatrix withthe following characteristics:◆the coefficients of the submatrix are all 0 (zero), 1 (one), or -1 (minus one);◆ each variable appears in at most two rows with at most one coefficient of +1 and at mostone coefficient of -1.ILOG CPLEX can perform different levels of extraction. The level it performs depends onthe NetFind parameter.◆◆When the NetFind parameter is set to 1 (one), ILOG CPLEX extracts only the obviousnetwork; it uses no scaling; it scans rows in their natural order; it stops extraction as soonas no more rows can be added to the network found so far.When the NetFind parameter is set to 2, the default setting, ILOG CPLEX also usesreflection scaling (that is, it multiplies rows by -1) in an attempt to extract a largernetwork.◆ When the NetFind parameter is set to 3, ILOG CPLEX uses general scaling, rescalingboth rows and columns, in an attempt to extract a larger network.In terms of total solution time expended, it may or may not be advantageous to extract thelargest possible network. Characteristics of your problem will qualify the tradeoff betweennetwork size and the number of simplex iterations required to finish solving the model aftersolving the embedded network.Even if your problem does not conform precisely to network conventions, the networkoptimizer may still be advantageous to use. When it is possible to transform the originalstatement of a linear program into network conventions by these algebraic operations:◆◆◆◆changing the signs of coefficients,multiplying constraints by constants,rescaling columns,adding or eliminating redundant relations,222 ILOG CPLEX 11.0 — USER’ S MANUAL