ILOG CPLEX 11.0 File Formats > > ILOG CPLEX File Formats > MPS File Format: Industry Standard > Quadratically Constrained Programs (QCP) in MPS Files |
Quadratically Constrained Programs (QCP) in MPS Files |
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As explained in the ILOG CPLEX User's Manual in Solving Problems with Quadratic Constraints (QCP), ILOG CPLEX can solve problems with quadratic terms among the constraints if the Q matrix for the quadratic term is positive semi-definite and the quadratic function defines a convex region. ILOG CPLEX has extended the MPS format to accommodate QCP models.
The quadratic constraints of such a model are listed in the ROWS
section, and their linear coefficients appear in the COLUMNS
section, just the same as coefficients from the linear constraints.
The quadratic terms go in QCMATRIX
sections, one QCMATRIX
per quadratic constraint. QCMATRIX
sections appear after the optional SOS
section. They may appear either after or before the QMATRIX
(objective) section.
The name of the constraint appears on the same line after QCMATRIX
.
The quadratic terms of the quadratic expression must be given as a symmetric matrix. That is, if there is an entry for Qij, then there must be an identical entry for Qji when i is not equal to j. This requirement is the same as for the QMATRIX
section, where any quadratic terms in the objective function are declared. The formats of the Q parts are the same.
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