DE optimization with equality constraint

Reply to "Optimization with constraint" on March 14, 2008

 One can get an accurate solutons applying the "Differential Evolution" algorithm
 as implemented in the DEoptim package:

    f2 <- function(x){
        if (x[1] + x[2] < 1 || x[1] + x[2] > 1) {
            r <- Inf
        } else {
            r <- x[1]^2 + x[2]^2
        }
        return(r)
    }

    lower <- c(0, 0)
    upper <- c(1, 1)

    DEoptim(f2, lower, upper, control=list(refresh=200))$bestmem

    iteration:  200 best member:  0.5 0.5 best value:  0.5

 This approach assumes nothing about the gradient, hessian or whatever. And the
 equality is split into two inequalities assuming no relaxation or penalty.

 Andreas Klein <klein82517 <at> yahoo.de> wrote:

 >
 > Hello.
 >
 > I have some problems, when I try to model an
 > optimization problem with some constraints.
 >
 > The original problem cannot be solved analytically, so
 > I have to use routines like "Simulated Annealing" or
 > "Sequential Quadric Programming".
 >
 > But to see how all this works in R, I would like to
 > start with some simple problem to get to know the
 > basics:
 >
 > The Problem:
 > min f(x1,x2)= (x1)^2 + (x2)^2
 > s.t. x1 + x2 = 1
 >
 > The analytical solution:
 > x1 = 0.5
 > x2 = 0.5
 >
 > Does someone have some suggestions how to model it in
 > R with the given functions optim or constrOptim with
 > respect to the routines "SANN" or "SQP" to obtain the
 > analytical solutions numerically?
 >
 > Again, the simple example should only show me the
 > basic working of the complex functions in R.
 >
 > Hope you can help me.
 >
 > With regards
 > Andreas.