On calculating analytic centers
By: Allen Goldstein
Contributors: Naval Postgraduate School (U.S.). Dept. of Mathematics
Publisher: Naval Postgraduate School; Available from National Technical Information Service
Published: 1989
Place of publication: Monterey, Calif; Springfield, Va
Language: eng
Subjects: COMPUTATIONS
Other titles: NPS-53-89-015.
Description: The analytic center of a polytope can be calculated in polynomial time by Newton's      method. This note was motivated by papers of Renegar and Shub(88) and by Ye(89).      We apply Smale's(86) estimates at one point for Newton's method to the problem of      finding the analytic center of a polytope. The method converges globally in the      appropriate norm. The ideas are then applied to obtain a possible benchmark for path      following methods. When Smale's method is tractable its power stems not only from the      fact that the information is concentrated at one point. There are 2 norms to estimate, not      3 as in the Kantorovich estimate. Moreover no estimate of the inverse of the derivative      operator by itself is needed. The need for the norm of the inverse by itself often makes for      coarse estimates. (kr)
Notes: Title from cover.

"NPS-53-89-015."

"August 1989."

AD A215 635.

Includes bibliographical references (p. 7).

aq/aq cc:9116 06/25/98