Andreas Klein <klein82517 <at> yahoo.de> writes: > > 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? >
In optimization problems, very often you have to replace an equality by two inequalities, that is you replace x1 + x2 = 1 with min f(x1,x2)= (x1)^2 + (x2)^2 s.t. x1 + x2 >= 1 x1 + x2 <= 1 The problem with your example is that there is no 'interior' starting point for this formulation while the documentation for constrOptim requests: The starting value must be in the interior of the feasible region, but the minimum may be on the boundary. You can 'relax', e.g., the second inequality with x1 + x2 <= 1.0001 and use (1.00005, 0.0) as starting point, and you will get a solution: >>> A <- matrix(c(1, 1, -1, -1), 2) >>> b <- c(1, -1.0001) >>> fr <- function (x) { x1 <- x[1]; x2 <- x[2]; x1^2 + x2^2 } >>> constrOptim(c(1.00005, 0.0), fr, NULL, ui=t(A), ci=b) $par [1] 0.5000232 0.4999768 $value [1] 0.5 [...] $barrier.value [1] 9.21047e-08 where the accuracy of the solution is certainly not excellent, but the solution is correctly fulfilling x1 + x2 = 1. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.