BQP Cuts

Type

Selection

Range

The settings listed below

Default

Automatic

This option controls the addition of cuts based on the Boolean Quadric Polytope (BQP) for nonconvex quadratic programs (QP) or nonconvex mixed integer quadratic programs (MIQP) solved to global optimality, that is, if the option Solution Target is set to ‘Search for global optimum’. Setting the value to “Automatic”, the default, indicates that the attempt to BQP cuts should continue only if it seems to be helping. Possible values are:

  • Off

  • Automatic

  • Generate cuts moderately

  • Generate cuts aggressively

  • Generate cuts very aggressively

BQP cuts exploit a cutting plane technique to solve QP or MIQP problems more efficiently. This technique is based on the observation that every valid linear cut for the mixed integer set defined by:

A = { (x, X) : x in {0,1}, X_ij = x_i x_j if i is different from j, X_ii = 0 }

is also a valid inequality for the continuous set defined by:

B = { (x, X) : 0 <= x <= 1, X_ij = x_i x_j if i is different from j, X_ii = 0 }

Note

  • CPLEX does not apply BQP cuts to mixed integer linear programs (MIP).

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