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" <[EMAIL PROTECTED]> 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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