Dieter Menne had already told you what the problem is. You have 2 local minima. One is a global minimum. Depending on your starting interval, the optimizer can converge to one of the two local minima. If you want to be reasonably sure that you always find the global minimum, you either have to use problem-specific knowledge or try a sufficiently large number of starting values and pick the best solution. Here is one approach:
require(BB) p0 <- matrix(rnorm(20), 20, 1) # 20 random starting values ans <- multiStart(par=p0, fn=f, action="optimize", P=c(0.99,1.01), U=c(1,0)) ans Hope this helps, Ravi. -----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org] On Behalf Of Michael Bernsteiner Sent: Wednesday, September 08, 2010 8:36 AM To: r-help@r-project.org Subject: [R] optimized value worse than starting Value Dear all, I'm optimizing a relatively simple function. Using optimize the optimized parameter value is worse than the starting. why? f<-function(delta,P,U){ minimiz<-P+delta*U x<-minimiz[1] y<-minimiz[2] z<-100*(y-x^2)^2+(1-x)^2 return(z) } result<-optimize(f, interval=c(-10, 10), P=c(0.99,1.01), U=c(1,0)) result Output: > result<-optimize(f, interval=c(-10, 10), P=c(0.99,1.01), U=c(1,0)) > result $minimum [1] -1.990015 $objective [1] 4.01 Function Value at Starting Point with free parameter=0: > f(0,c(0.99,1.01),c(1,0)) [1] 0.089501 It seems as if optimize doesn't check the whole interval. > result<-optimize(f, interval=c(-1, 10), P=c(0.99,1.01), U=c(1,0)) > result $minimum [1] 0.01497394 $objective [1] 2.481504e-05 Changing the lower interval value leads to the result I am looking for. How do I find this result when I have no idea where the optimal values lies and want to look in an interval that is as wide as possible? any ideas? Michael [[alternative HTML version deleted]] ______________________________________________ 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. ______________________________________________ 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.
