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

[Gabor Grothendieck]

Correction.

Yes, it's the projection of S onto the subspace orthogonal to B which is:

X <- S - (B%o%B) %*% S/ 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 1:11 PM, Gabor Grothendieck <ggrothendieck at gmail.com
> wrote:

> 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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>
>
>
> --
> Statistics & Software Consulting
> GKX Group, GKX Associates Inc.
> tel: 1-877-GKX-GROUP
> email: ggrothendieck at gmail.com
>



-- 
Statistics & Software Consulting
GKX Group, GKX Associates Inc.
tel: 1-877-GKX-GROUP
email: ggrothendieck at gmail.com

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