Newton-secant methods with values in a cone

2017 ◽  
pp. 271-281
Author(s):  
Ioannis K. Argyros ◽  
Á. Alberto Magreñán
Keyword(s):  
Secant Methods

An All-Inclusive Efficient Region of Updates for Least Change Secant Methods

1995 ◽  
Vol 5 (1) ◽  
pp. 172-191 ◽  
Author(s):  
Henry Wolkowicz ◽  
Qing Zhao
Keyword(s):  
Secant Methods

scholarly journals Graphical representation of the application of the bisection and secant methods for obtaining roots of equations using Matlab

2018 ◽  
Vol 1053 ◽  
pp. 012026
Author(s):  
Nancy Velasco ◽  
Dario Mendoza ◽  
Vicente Hallo ◽  
Elizabeth Salazar-Jácome ◽  
Victor Chimarro
Keyword(s):  
Graphical Representation ◽  
Secant Methods ◽  
Roots Of Equations

scholarly journals A family of global convergent inexact secant methods for nonconvex constrained optimization

2018 ◽  
Vol 12 (2) ◽  
pp. 165-176
Author(s):  
Zhujun Wang ◽  
Li Cai ◽  
Zheng Peng
Keyword(s):  
Global Convergence ◽  
Constrained Optimization ◽  
Line Search ◽  
Merit Function ◽  
Exact Penalty ◽  
Search Technique ◽  
Nonconvex Constrained Optimization ◽  
Secant Methods ◽  
Armijo Line Search ◽  
Line Search Technique

We present a family of new inexact secant methods in association with Armijo line search technique for solving nonconvex constrained optimization. Different from the existing inexact secant methods, the algorithms proposed in this paper need not compute exact directions. By adopting the nonsmooth exact penalty function as the merit function, the global convergence of the proposed algorithms is established under some reasonable conditions. Some numerical results indicate that the proposed algorithms are both feasible and effective.

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