Conference rusure::math

1754.0. "Projection of a point on a cone??" by MR4DEC::RICARD () Tue May 25 1993 23:57

We are given a cone, C, defined as C = {x | x = Py, for some y >= 0} 
(where P is an n x n real matrix and y is a real vector of length n) 
and a point d.  Assume that d is not in C.

What is the projection of d onto the set C?  The projection is the 
point, y, that minimizes:

	min |y - d|
	
	subject to y in C

where | | is the Euclidean norm.

Thanks in advance for any ideas or references,

Mike

    In 3-space, a cone is given as a function of 2 free variables.  In your
    case, you describe a 'cone' in n-space with n free variables (the elements
    of vector y).