[net.math] Karmarkar's algorithm: A quote from _Scientific American_

gtsc@dmcnh.UUCP (12/28/84)

kill -9 `pid(bug)`

The following is an excerpt from _Scientific American_, January, 1985;
In the section "Science and the Citizen" under the title "Simplified
Simplex" pp. 54-55:

	...Now Narendra Karmarkar of AT&T Bell Laboratories has invented
	a new algorithm that appears to solve such [linear programming]
	problems much faster than the simplex does....
	...Five years ago four mathematicians in the U.S.S.R. devised an
	algorithm called the ellipsoid method that is faster than the simplex
	method for certain rather artificial problems.  In practice, however,
	such problems almost never arise, and almost all practical problems
	are solved many times faster by the simplex method than they are
	by the ellipsoid.
	Karmarkar's algorithm seems to win on both counts.  It appears to
	improve on the practical performance of the simplex algorithm, and
	its theoretical, "worst case" performance is better than that of the
	ellipsoid method.
	...It picks a starting point on the polygon and then attempts to
	improve the profit by taking a short cut through the polygon rather
	than merely moving along some edge....The Karmarkar algorithm is now
	being translated into high-speed machine language so that its full
	capabilities can be more fairly compared with those of the simplex.

Apparently it is the ellipsoid method that was so heralded but bombed.  The
Karmarkar method seems to be catching on.
Anyone have the method?  Bell Labs must have published one of their little
booklets on it.
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