Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: notesfiles
Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!tektronix!hplabs!hp-pcd!hplvle!drick
From: drick@hplvle.UUCP (drick)
Newsgroups: net.math
Subject: re: Karmarkar algorithm
Message-ID: <7700001@hplvle.UUCP>
Date: Wed, 2-Jan-85 22:00:00 EST
Article-I.D.: hplvle.7700001
Posted: Wed Jan  2 22:00:00 1985
Date-Received: Sat, 12-Jan-85 08:33:28 EST
Organization: Hewlett-Packard - Loveland, CO
Lines: 37
Nf-ID: #N:hplvle:7700001:000:1468
Nf-From: hplvle!drick    Jan  2 19:00:00 1985

[bug food]

Karmarkar's paper has not been published yet.  Our facility librarian
was able to get me a copy of it by calling Bell Labs.  Whoever she
talked to also sent along a four page monograph (author unknown)
which answers the question: "Why is the new algorithm better than
the simplex method and the ellipsoid method?"

A couple of interesting points from the monograph:

1.  "A direct comparison of cpu times shows that the new method beats
MPSX/370 - a commercial implementation of the simplex method - by more
that a factor of 50 on problems with several thousand variables.  
Moreover, the relative advantage over the simplex method grows with
the size of the problem."

2.  As with the simplex algorithm, there is a gap between its worst-
case behavior and its average behavior in actual use.

3.  The algorithm is "easily" extended to nonlinear convex programming
problems.

4.  The existence of this algorithm reestablishes Turing's model of
computation.  Briefly, Turing said a "good" algorithm is a polynomial-
time algorithm.  The only previously known polynomial-time algorithm
for linear programming, the ellipsoid method, was slower in practice
than the simplex method (an exponential-time method), thus casting
doubt on Turing's conjecture.

I don't know when Karmarkar's paper is scheduled for publication.  I got
my pre-publication copy on October 1.

David L. Rick
Loveland Instrument Division
Hewlett-Packard Company

hplabs!hplvla!hplvle