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