ILOG CPLEX .NET Reference Manual

Cplex.QpIndefCertificate Method 

Returns a vector proving that the Q matrix of QP is not positive semi-definite.

public virtual void QpIndefCertificate(
   INumVar[] var,
   double[] x
);

Parameters

var
An array of length getNcols where the variables of the active model are returned.
x
An array of length getNcols. By setting var[j] to x[j] for all variables, the quadratic term of the objective function evaluates to a negative value.

Remarks

When solving QPs, the quadratic terms of the objective function must form a positive semi-definite Q matrix (for a minimization problem, or negative semi-definite otherwise). If Cplex finds this not be true, it will discontinue the optimization. In such cases, this method can be used to compute assignments to all variables such that the quadratic term of the objective function evaluates to a negative value (x'Q x < 0 in matrix terms) to prove the indefiniteness.

See Also

Cplex Class | ILOG.CPLEX Namespace