R help - Sep 2011 - Imposing Feller condition using project constraint in spg

Dear R-users,

I'm running a maximization problem in which I want to impose a condition on
the relationship between 2 parameters.
The condition is that w[4] = (1+eps)/(2*w[1]), or equivalently w[4]*w[1]
(1+eps)/2 , where eps is some small positive constant.

I've been trying to formulate a function that takes care of this, but I
can't really make it work so any suggestions would be much appreciated.

Thank you.

Kristian Lind

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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: rvaradhan@jhmi.edu<mailto:rvaradhan@jhmi.edu>


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