Expanding the applicability of the Gauss–Newton method for convex optimization under a majorant condition

SeMA Journal ◽  
2014 ◽  
Vol 65 (1) ◽  
pp. 37-56 ◽  
Author(s):  
Á. Alberto Magreñán ◽  
Ioannis K. Argyros
Keyword(s):  
Convex Optimization ◽  
Newton Method ◽  
Majorant Condition

A proximal-Newton method for unconstrained convex optimization in Hilbert spaces

Optimization ◽  
2017 ◽  
Vol 67 (1) ◽  
pp. 67-82 ◽  
Author(s):  
M. Marques Alves ◽  
Benar F. Svaiter
Keyword(s):  
Convex Optimization ◽  
Newton Method ◽  
Hilbert Spaces

scholarly journals On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Fangqin Zhou
Keyword(s):  
Convergence Analysis ◽  
Newton Method ◽  
Local Convergence ◽  
Singular Systems ◽  
Inexact Newton Method ◽  
Systems Of Equations ◽  
Convergence Ball ◽  
Special Cases ◽  
Majorant Condition ◽  
Local Convergence Analysis

We present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the singular systems. It also allows us to obtain an estimate of convergence ball for inexact Newton method and some important special cases.

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