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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