One (very crude) approach would be to take DE or SA optimisers and introduce
constraints like (a + b - 2)^1000 in your target SSE function
> On 17 Aug 2015, at 18:25, Mark Leeds <marklee...@gmail.com> wrote:
>
> Hi Eric: A friend of mine pointed out that my answer to your question about
> constraining the regression is incorrect because the way I recommended
> bounding the parameters won't guarantee feasibility.
>
> Below is a small example that implements what I described but note that the
> sum constraint won't necessarily hold if the other 2 parameters end up both
> being greater than 0.5. ( it does in this example I created but that's just
> fortunate ). So don't use my approach.
>
> There are probably optimizers out there that handle sum constraints. One
> that does but I have little experience with it is Ravi Varadhan's BB
> package. Also, check out John Nash's book
> if you have it because that gives nice coverage of a lot ( if not all ) of
> all of the optimization packages available in R.
>
> Or as you noted, there is probably an R package that estimates that type of
> regression directly. Good luck and sorry for noise.
>
> #====================================================================
>
> set.seed(123)
> x1 <- rnorm(1000)
> x2 <- rnorm(1000)
> x3 <- rnorm(1000)
> y <- rnorm(1000, 2 + .5 * x1 + .3 * x2 + .2 * x3)
>
> residsfunc <- function(par, x1,x2,x3,y) {
> Xmod <- cbind(par[1], par[2]*x1, par[3]*x2, (1-par[2]-par[3])*x3)
> sum((y - Xmod)^2)
> }
>
> mypar <- c(mean(y),0.9,0.9)
>
> result <- optim(par = mypar, fn=residsfunc, method = "L-BFGS-B", lower =
> c(0,0,0), upper = c(Inf,1,1),
> x1 = x1, x2 = x2, x3 = x3, y = y)
>
> lastpar <- 1-result$par[2]-result$par[3]
> print(c(result$par,lastpar))
>
> [[alternative HTML version deleted]]
>
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