Nonlinear constraint

[ursula challita]

Hello all,

I want to check whether the solvers in AIMMS solve non-linear problems or if 

anyone can suggest a way to linearize this constraint.

The nonlinear constraint is attached.

Thanks in advance for the help.

Ursula

[Luis Pinto]

There are non-linear solvers in AIMMS (I don't work with non-linear, but I beleive Baron and Mosek are examples right?).

Not sure about the linearization... what are the variables?

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[ursula challita]

Thanks Luis.

I've attached an updated form of my constraint.

I am looking for a solution approach, either using a non-linear solver or trying to linearize this objective.

I would appreciate any suggestion.

Thanks,

Ursula

[Vinay Sewdien]

Hi Ursula,

The Identifier in which you have defined your mathematical problem has the option to chose the type of solver. I guess in your case it would be the nonlinear program NLP...

[ursula challita]

Thanks Vinay.

I wanted to check whether the solvers in AIMMS could solve such a problem.

[Marcel Hunting]

Hi,

I don't think there exists an equivalent linear formulation for your nonlinear constraint. Your problem appears to have binary variables and therefore the mathematical programming type becomes Mixed Integer Nonlinear Programming (MINLP) which is supported by the solvers AOA, BARON and Knitro in AIMMS. If your problem is non-convex (which it seems to be) then AOA and Knitro will only return a local optimum. BARON is a global solver but might take a long time to run. Unfortunately, BARON and Knitro are not available in the free academic license. An examples of running with AOA can be found in this AIMMS blog article: http://blog.aimms.com/2012/02/solving-minlp-problems-with-aimms-outer-approximation/ .

Marcel Hunting

AIMMS Software Developer

[ursula challita]

Hi Marcel,

Thanks a lot for the support.

Actually I was able to simplify the constraint further. The simplified version is attached.

I want to check also how can I get the license for Baron.

Many Thanks!

Ursula

[Guido Diepen]

Hi Ursula,

Baron is not included in the free academic license program of AIMMS.

If you want to have access to Baron, you will have to go for a paid academic license. For more details see our website: http://www.aimms.com/academic/paid-academic-license

Guido Diepen

AIMMS Specialist

[Marcel Hunting]

Hi Ursula,

What are the I_k and the I_j in the (1 - c_k I_k / I_j ) term? I assume that c_k and s_pi are the only variables in this constraint; is that correct?

Best regards,

Marcel

[Ursula]

Hello Marcel,

Indeed, c_i and s_pi are the binary variables in the problem.

I_k and I_j are parameters. 

Is there any approach that can linearize this objective?

Thanks for the help.

Ursula

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[Marcel Hunting]

Hi Ursula,

If I_k and I_j are 0/1 parameters then it would maybe be possible to linearize the constraint. If they are not then I see no way to linearize it.

Best regards,

Marcel

[Ursula]

Hi Marcel,

The parameters are not bounded. They take continuous values.

Maybe i'll try to solve it using a non-linear solver.

Thanks a lot for the support.

Ursula

[ursula challita]

Hello,

I want to check whether Baron is available in the free trial license?

Many Thanks!

Ursula

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[Guido Diepen]

Hi Ursula,

Baron is indeed available in the free trial.

Guido Diepen

AIMMS Specialist

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[ursula challita]

Hi Guido,

I installed a free trial license. Baron does not appear in the list of solvers.

How can I set it to be my default solver?

Many Thanks,

Ursula

[Guido Diepen]

Hi Ursula,

you  might have to install the Baron solver in the solver configuration screen. More information about how to install a new solver can be found in the Users Guide. You can find the details in the current version that is online  in Section 22.3 of http://www.aimms.com/aimms/download/manuals/aimms3ug_projectsettingsandoptions.pdf

Guido Diepen

AIMMS Specialist

[ursula challita]

Hi Guido,

Thanks a lot.

Ursula