[AMPL 24463] Error

Hello everyone,

I’m facing an issue for days. Could you please help me?

QP Hessian is not positive semi-definite.
0 MIP simplex iterations
0 branch-and-bound nodes
No basis.

“QP Hessian is not positive semi-definite” says that you have some quadratic terms in your model – where a variable is multiplying another variable. It also says that some of your quadratic terms are not convex (mathematically, they do not have the “positive semi-definite” property); as a result, CPLEX is not accepting your quadratic problem, and is not trying to solve it.

To see if you can get CPLEX to accept your problem, give the command

option cplex_options 'reqconvex=3';

before solving (or if you are already defining a cplex_options string, addreqconvex=3 to it). This will tell CPLEX to try to use a more advanced algorithm to compute a global optimum for your quadratic problem. If you do this and you still get the “QP Hessian is not positive semi-definite” message, however, then your model has some non-convex quadratic constraints that CPLEX cannot handle.