Hi Ravi,
Thank you for your reply and please excuse my late response.
Plugging w2 = k/w1 from (A) into (B) yields
(C) f(w1') = (w1-w1)^2 + (w2-k/w1)^2
The partial derivative wrt w1' is
(D) df(w1')/ dw1' = -2(w1-w1) + 2(w2-k/w1)*k/(w1')^2
in order for this to be a minimum the f.o.c. df(w1')/ dw1' = 0 and the
s.o.c. d^2f(w1')/ d(w1')^2 >0 must be satisfied.
I follow you on substituting the constraint into the distance from the
iterate to (w1', w2') and then minimizing this distance, but I'm not quite
sure how to turn this into a projection function. Any suggestions?
Regards,
Kristian
2011/9/8 Ravi Varadhan <rvarad...@jhmi.edu>
> Hi Kristian,****
>
> ** **
>
> The idea behind projection is that you take an iterate that violates the
> constraints and project it onto a point such that it is the nearest point
> that satisfies the constraints. ****
>
> ** **
>
> Suppose you have an iterate (w1, w4) that does not satisfy the constraint
> that w1 * w4 != (1 + eps)/2. Our goal is to find a (w1, w2), given (w1,
> w2), such that****
>
> ** **
>
> **(A) **w1 * w2 = (1+eps)/2 = k****
>
> **(B) **(w1-w1)^2 + (w2-w2)^2 is minimum. ****
>
> ** **
>
> This is quite easy to solve. We know (w1, w2). You plug in w2 = k/w1
> from (A) into (B) and minimize the function of w1. This is a simple
> calculus exercise, and I will leave this as a homework problem for you to
> solve!****
>
> ** **
>
> Best,****
>
> Ravi.****
>
> ** **
>
> -------------------------------------------------------****
>
> Ravi Varadhan, Ph.D.****
>
> Assistant Professor,****
>
> Division of Geriatric Medicine and Gerontology School of Medicine Johns
> Hopkins University****
>
> ** **
>
> Ph. (410) 502-2619****
>
> email: rvarad...@jhmi.edu****
>
> ** **
>
[[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.
