Quadratically constrained programs (QCP) in MPS files

CPLEX extensions of MPS file format support quadratically constrained programs.

As explained in the CPLEX User’s Manual in Solving problems with quadratic constraints (QCP), 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. 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 Q_ij, then there must be an identical entry for Q_ji 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.