Simple examples for the failure of Newton’s method with line search for strictly convex minimization

2015 ◽  
Vol 158 (1-2) ◽  
pp. 23-34 ◽  
Author(s):  
Florian Jarre ◽  
Philippe L. Toint
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Line Search ◽  
Convex Minimization ◽  
Strictly Convex

Solving algebraic Riccati equations on parallel computers using Newton's method with exact line search

2000 ◽  
Vol 26 (10) ◽  
pp. 1345-1368 ◽  
Author(s):  
Peter Benner ◽  
Ralph Byers ◽  
Enrique S Quintana-Ortı́ ◽  
Gregorio Quintana-Ortı́
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Line Search ◽  
Riccati Equations ◽  
Parallel Computers ◽  
Algebraic Riccati Equations ◽  
Exact Line Search

Optimal Power Flow Using Newton’s Method

2012 ◽  
Vol 3 (2) ◽  
pp. 167-169
Author(s):  
F.M.PATEL F.M.PATEL ◽  
◽  
N. B. PANCHAL N. B. PANCHAL
Keyword(s):  
Newton’S Method ◽  
Newton's Method ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Optimal Power

An Efficient Sixth-Order Convergent Newton-Type Iterative Method for Nonlinear Equations

2012 ◽  
Vol 220-223 ◽  
pp. 2585-2588
Author(s):  
Zhong Yong Hu ◽  
Fang Liang ◽  
Lian Zhong Li ◽  
Rui Chen
Keyword(s):  
Iterative Method ◽  
Nonlinear Equations ◽  
Newton’S Method ◽  
Newton's Method ◽  
Efficiency Index ◽  
Sixth Order ◽  
Type Method ◽  
Second Derivatives ◽  
Better Than

In this paper, we present a modified sixth order convergent Newton-type method for solving nonlinear equations. It is free from second derivatives, and requires three evaluations of the functions and two evaluations of derivatives per iteration. Hence the efficiency index of the presented method is 1.43097 which is better than that of classical Newton’s method 1.41421. Several results are given to illustrate the advantage and efficiency the algorithm.

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