ERROR 10020: Objective Q not PSD and ERROR 10021: Quadratic equality constraints

Gurobi versions 9.0 and later can solve models with non-convex quadratic constraints and objectives. However, you may encounter one of the following errors when solving a non-convex quadratic problem:

Error 10020: Objective Q not PSD
Error 10021: Quadratic equality constraints

By default, Gurobi only solves a non-convex quadratic problem if the non-convex quadratic constructs can be removed or linearized during presolve.

To resolve this issue, set the NonConvex parameter to 2.

With this parameter setting, Gurobi solves non-convex quadratic problems by translating them into bilinear form, then applying spatial branching. Enforcing this parameter change should make you aware of the added complexity of the model.

Further information

• Gurobi Reference Manual: Quadratic Constraints
• Webinar on Non-Convex Quadratic Optimization