Square Root (sqrt) in the Objective Function

[Nadja Herger]

Dear Community,

Is it possible to have a square root (sqrt() or math.sqrt() or ()**0.5 or ...) in the objective function of a Pyomo ConcreteModel? I assume that it depends on the solver and so far I have tried solver=glpk, cplex and gurobi. 

I obtain the following error message when using all three solvers: 

Cannot write legal LP file.  Objective 'OBJ' has nonlinear terms that are not quadratic.

Is there a Pyomo-compatible solver that can deal with nonlinear terms?

My goal is to minimize the root-mean-square error (RMSE). I formulate my Objective as follows:

model.OBJ = Objective(expr = sqrt( np.mean( [(error[i]**2)*model.x[i] for i in range(N_models)] ) ) )

I wonder if the sqrt() part is even necessary or if the optimization algorithm would end up with the same solution if I defined my Objective as the mean squared error (MSE) instead, as such:

model.OBJ = Objective(expr = np.mean( [(error[i]**2)*model.x[i] for i in range(N_models)] ))

Any ideas?

Thanks for your help!

Kind regards,

Nadja

[Braulio Brunaud]

Hello

All the solvers you tried are linear. If you have a square root in the objective function the model is nonlinear and you would need to use a nonlinear solver such as ipopt. Also, when solving an NLP you  need to provide a starting point.

You can download the binaries from:
http://ampl.com/products/solvers/open-source/

regards

Braulio

[Gabe Hackebeil]

Also, your intuition is correct in that you do not need to take the square root.

Gabe

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[Nadja Herger]

Hi Braulio and Gabe,

Thanks for your help!

Good to know that there are also solvers around which can deal with nonlinear objective functions. I'll stick to the linear solvers for now, as my problem becomes linear if I forget about the square root. 

Regards,

Nadja

[William Hart]

The derivative is linear, but the objective is quadratic...

--Bill

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