On Wed, 4 Nov 2009 14:48:08 -0800 (PST) s t <thamp...@yahoo.com> wrote:
> I'm trying to do the following constrained optimization example. > Maximize x1*(1-x1) + x2*(1-x2) + x3*(1-x3) > s.t. x1 + x2 + x3 = 1 > x1 >= 0 and x1 <= 1 > x2 >= 0 and x2 <= 1 > x3 >= 0 and x3 <= 1 > which are the constraints. > I'm expecting the answer x1=x2=x3 = 1/3. This is a quadratic programming problem (mininimising/maximising a quadratic function under linear equality and inequality constraints). There are several R packages that solve such problems, e.g.: R> library(quadprog) R> Dmat <- diag(3) R> dvec <- rep(1,3)/3 R> Amat <- cbind(rep(1,3), diag(3), -diag(3)) R> bvec <- c(1, rep(0,3), rep(-1,3)) R> solve.QP(Dmat, dvec, Amat, bvec, meq=1) $solution [1] 0.3333333 0.3333333 0.3333333 $value [1] -0.1666667 $unconstrainted.solution [1] 0.3333333 0.3333333 0.3333333 $iterations [1] 2 0 $iact [1] 1 You may want to consult: http://cran.r-project.org/web/views/Optimization.html HTH. Cheers, Berwin ========================== Full address ============================ Berwin A Turlach Tel.: +61 (8) 6488 3338 (secr) School of Maths and Stats (M019) +61 (8) 6488 3383 (self) The University of Western Australia FAX : +61 (8) 6488 1028 35 Stirling Highway Crawley WA 6009 e-mail: ber...@maths.uwa.edu.au Australia http://www.maths.uwa.edu.au/~berwin ______________________________________________ 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.
