[R] Nonlinear constrains with optim

[Spencer Graves]

Hi, Patrick, Paul, et al.: 

<see in line>     

Patrick Burns wrote:
> I don't know of any sources, but the idea is quite simple.
>
> For each constraint that is broken, the penalty is the amount
> by which the constraint is broken times a penalty rate.  The
> total penalty to add to the objective is the sum of penalties
> over all constraints.
>
> There is a catch or two when using this with derivative-based
> optimizers.  The objective typically becomes non-differentiable
> at the boundary, and optimizers can get confused.  
I believe I've gotten good results with penalties that are the SQUARE of 
the amount by which the constraints were violated.  These are 
continuously differentiable and so don't confuse the derivative-based 
optimizers much. 

Also, I start with a small penalty, then increase the penalty until I 
get a solution that seems sensible.  If you can't handle a solution just 
a little outside your constraints, shrink a little the place at which 
the penalty starts. 

      Hope this helps. 
      Spencer Graves

> They might
> be less confused with smaller penalty rates.  However if the
> penalty rate is too small, then you can get a "solution" that breaks
> one or more penalties.
>
> Starting from a solution given by Rgenoud or its ilk is probably
> a good idea.
>   
> Patrick Burns
> patrick at burns-stat.com
> +44 (0)20 8525 0696
> http://www.burns-stat.com
> (home of S Poetry and "A Guide for the Unwilling S User")
>
> Paul Smith wrote:
>
>   
>> Dear All
>>
>> I am dealing at the moment with optimization problems with nonlinear
>> constraints. Regenoud is quite apt to solve that kind of problems, but
>> the precision of the optimal values for the parameters is sometimes
>> far from what I need. Optim seems to be more precise, but it can only
>> accept box-constrained optimization problems. I read in the list
>> archives that optim can also be used with nonlinear constrains through
>> penalizations. However, I am not familiar with the technique of
>> penalizations. Could someone please indicate to me a site or a book to
>> learn about that penalization technique?
>>
>> Thanks in advance,
>>
>> Paul
>>
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>>  
>>
>>     
>
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>