Yes, it's the projection of S onto the subspace orthogonal to B which is: X <- S - B%*%B / sum(B*B)
and is also implied by Duncan's solution since that is what the residuals of linear regression are. On Tue, Oct 20, 2015 at 1:00 PM, Paul Smith <phh...@gmail.com> wrote: > On Tue, Oct 20, 2015 at 11:58 AM, Andy Yuan <yuan...@gmail.com> wrote: > > > > Please could you help me to select the most appropriate/fastest function > to use for the following constraint optimisation issue? > > > > Objective function: > > > > Min: Sum( (X[i] - S[i] )^2) > > > > Subject to constraint : > > > > Sum (B[i] x X[i]) =0 > > > > where i=1…n and S[i] and B[i] are real numbers > > > > Need to solve for X > > > > Example: > > > > Assume n=3 > > > > S <- c(-0.5, 7.8, 2.3) > > B <- c(0.42, 1.12, 0.78) > > > > Many thanks > > I believe you can solve *analytically* your optimization problem, with > the Lagrange multipliers method, Andy. By doing so, you can derive > clean and closed-form expression for the optimal solution. > > Paul > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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. > -- Statistics & Software Consulting GKX Group, GKX Associates Inc. tel: 1-877-GKX-GROUP email: ggrothendieck at gmail.com [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.