[R] Most appropriate function for the following optimisation issue?

[Gabor Grothendieck]

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 <phhs80 at gmail.com> wrote:

> On Tue, Oct 20, 2015 at 11:58 AM, Andy Yuan <yuan007 at 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
>
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