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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1754.0. "Projection of a point on a cone??" by MR4DEC::RICARD () Wed May 26 1993 02:57


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
T.RTitleUserPersonal
Name
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1754.1Is something missing?CFSCTC::GILBERTTue Oct 05 1993 14:593
    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).