[R] linear constraint optim with bounds/reparametrization

[Spencer Graves]

	  If A%*%theta>c, then log(c-A%*%theta) returns NA.  if A%*%theta<c, log(A%*%theta-c) returns NA.  Only when A%*%theta==c do you get a "number" from log(A%*%theta-c), and that's (-Inf).  

	  However, for an equality constraint, I've had good luck by with an objective function that adds something like the following to my objective function:  

	  constraintViolationPenalty*(A%*%theta-c)^2,  

where "constraintViolationPenalty" is passed via "..." in a call to optim.  If I want only (A%*%theta>=c), then I might write this as follows:  

	  constraintViolationPenalty*(A%*%theta<c)*(A%*%theta-c)^2  

           This term is everywhere differentiable and is 0 when the 
constraint is satisfied. 

            I may first run optim with a modest value for 
constraintViolationPenalty then restart it with the output of the 
initial run as starting values and with a larger value for 
constraintViolationPenalty. 

      hope this helps.  spencer graves

Ingmar Visser wrote:

>On 8/9/04 4:52 PM, "Thomas Lumley" <tlumley at u.washington.edu> wrote:
>
>  
>
>>On Mon, 9 Aug 2004, Kahra Hannu wrote:
>>
>>    
>>
>>>>1) constrOptim does not work in this case because it only fits inequality
>>>>constraints, ie A%*%theta > =  c
>>>>        
>>>>
>>>                          --- I was struggling with the same problem a
>>>few weeks ago in the portfolio optimization context. You can impose
>>>equality constraints by using inequality constraints >= and <=
>>>simultaneously. See the example bellow.
>>>
>>>      
>>>
>>Ick. You do not want to use constrOptim for equality constraints.
>>constrOptim is a log-barrier interior-point method, meaning that it adds
>>a multiple of log(A%*%theta-c) to the objective function. This is a really
>>bad idea as a way of faking equality constraints.
>>
>>Use Lagrange multipliers and optim.
>>    
>>
>
>Is there a package that does all that for me? Or is there example code that
>does something similar?
>
>ingmar
>
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