Can Gurobi solve non-linear optimization with non-linear constraints?

[Sina Porsa]

Hi everyone,

I am trying to solve an optimization problem and I was wondering if Gurobi is a good option or not.

The optimization problem has ~15000 parameters and ~15000 constraints. The objective function and all of the constraints are algebraic, highly non-linear functions. The parameters are all real numbers bounded between a lower band and an upper band and they can be discretized. According to the physics of the problem, I can easily find an initial guess which satisfies all of the constraints ans is fairly close to the global minimum/maximum. 

I was wondering if Gurobi is capable of handling this type of optimization problems? 

Thanks

Sina

[Jakob Sch.]

Hi Sina,

Short answer: No.
Longer answer: Gurobi is capable of solving convex quadratic problems, i.e. quadratic cost function with constraints of the form x^TQx +b^Tx + c <= 0 or x^Tx <= y or x^Tx <= y*z (with Q positive semidefinite, or conic constraints). If your problem only consists of constraints of this type, you can use gurobi.
Otherwise you might want to look at some special non-linear solver (Ipopt for example). You might also want to try some modeling language (for example GAMS or AMPL) that provide some interface for nonlinear solvers (both local optimizers and global optimizer).

Best regards,

Jakob