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From: dgc@ucla-cs.UUCP
Newsgroups: net.math
Subject: Karmaker Linear Programming Algorithm
Message-ID: <2820@ucla-cs.ARPA>
Date: Sun, 16-Dec-84 14:25:47 EST
Article-I.D.: ucla-cs.2820
Posted: Sun Dec 16 14:25:47 1984
Date-Received: Wed, 19-Dec-84 00:42:08 EST
Distribution: net
Organization: UCLA Computer Science Department
Lines: 42

[]

The Karmaker Algorithm appears in the  "Proceedings of the Sixteenth
Annual ACM Symposium on Theory of Computing" (1984), pp 302-311.
It can be ordered from the

    ACM Order Department
    P.O. Box 64145
    Baltimore, MD 21264

Its ACM order number is 508840 and its ISBN number is 0-89791-133-4. 
Cost to ACM members is $29.00 and to all others is $38.00.  It is
available in most research libraries which cover computer science or
mathematics.

There has been a great deal of media "hype" on this algorithm, somewhat
similar to the hype which followed the Khatchian alogrithm 4 years
ago, and which turned out to be highly exaggerated.  The value of the
Karmaker algorithm remains to be seen.

For another viewpoint, here is a comment by Walter Murray of Stanford
University.  It was distributed to the Numerical Analysis Community by
Gene Golub:

	"Some recent bboard messages have referred to linear
	programming.  The algorithm by Karmarkar is almost identical
	with iterative reweighted least squares (IRLS).  This latter
	algorithm is used to solve approximation problems other than
	in the l-2 norm.  It can be shown that the form of LP assumed
	by Karmarkar is equivalent to an l-infinity approximation
	problem.  If this problem is then solved by the IRLS algorithm
	the estimates of the solution generated are identical to those
	of the Karmarkar algorithm (assuming certain free choices in
	the definition of the algorithms).  Perhaps it should be added
	that the algorithm is not held in high regard in approximation
	circles.  To solve a an l-infinity problem it is usually
	transformed to an LP and solved using the simplex method."

David G. Cantor

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