Please use this identifier to cite or link to this item:
Title: Superlinear convergence of a Newton-type algorithm for monotone equations
Authors: Zhou, G.
Toh, K.C. 
Keywords: Convex minimization
Global convergence
Monotone equations
Newton method
Superlinear convergence
Issue Date: Apr-2005
Source: Zhou, G., Toh, K.C. (2005-04). Superlinear convergence of a Newton-type algorithm for monotone equations. Journal of Optimization Theory and Applications 125 (1) : 205-221. ScholarBank@NUS Repository.
Abstract: We consider the problem of finding solutions of systems of monotone equations. The Newton-type algorithm proposed in Ref. 1 has a very nice global convergence property in that the whole sequence of iterates generated by this algorithm converges to a solution, if it exists. Superlinear convergence of this algorithm is obtained under a standard nonsingularity assumption. The nonsingularity condition implies that the problem has a unique solution; thus, for a problem with more than one solution, such a nonsingularity condition cannot hold. In this paper, we show that the superlinear convergence of this algorithm still holds under a local error-bound assumption that is weaker than the standard nonsingularity condition. The local error-bound condition may hold even for problems with nonunique solutions. As an application, we obtain a Newton algorithm with very nice global and superlinear convergence for the minimum norm solution of linear programs. © 2005 Springer Science+Business Media, Inc.
Source Title: Journal of Optimization Theory and Applications
ISSN: 00223239
DOI: 10.1007/s10957-004-1721-7
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.


checked on Feb 28, 2018


checked on Feb 19, 2018

Page view(s)

checked on Mar 12, 2018

Google ScholarTM



Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.