An edition of How good are Global Newton methods? (1988)
How good are Global Newton methods?
By Allen A. Goldstein
Publish Date
1988
Publisher
Naval Postgraduate School,Available from National Technical Information Service
Language
eng
Pages
-
Description:
Pt.1. 1) Relying on a theorem of Nemerovsky and Yuden(1979) a lower bound is given for the efficiency of global Newton methods over the class C1(mu, Lambda). 2) The efficiency of Smale's global Newton method in a simple setting with a nonsingular, Lipschitz-continuous Jacobian is considered. The efficiency is characterized by 2 parameters, the condition number Q and the smoothness S. The efficiency is sensitive to S, and insensitive to Q. Keywords: Unconstrained optimization, Computational complexity, Algorithms. (JD)--Pt. 2. Newton's method applied to certain problems with a discontinuous derivative operator is shown to be effective. A global Newton method in this setting is exhibited and its computational complexity is estimated. As an application a method is proposed to solve problems of linear inequalities (linear programming, phase 1). Using an example of the Klee-Minty type due to Blair, it was found that the simplex method (used in super-lindo) required over 2,000 iterations, while the method above required an average of 8 iterations (Newton steps) over 15 random starting values. Keywords; Linear programming; Computational complexity. (JHD)