Convergence properties of a restricted Newton-type method for generalized equations with metrically regular mappings

2017 ◽  
pp. 1-21 ◽  
Author(s):  
M. H. Rashid ◽  
Ya-xiang Yuan
Keyword(s):  
Generalized Equations ◽  
Convergence Properties ◽  
Type Method

scholarly journals Convergence Properties of Extended Newton-type Iteration Method for Generalized Equations

2018 ◽  
Vol 10 (4) ◽  
pp. 1
Author(s):  
M. Khaton ◽  
M. Rashid ◽  
M. Hossain
Keyword(s):  
Banach Spaces ◽  
Local Convergence ◽  
Iteration Method ◽  
Generalized Equation ◽  
Generalized Equations ◽  
Convergence Properties ◽  
Closed Graph ◽  
Point Bar ◽  
Type Method ◽  
Set Valued Mapping

In this paper, we introduce and study the extended Newton-type method for solving generalized equation $0\in f(x)+g(x)+\mathcal F(x)$, where $f:\Omega\subseteq\mathcal X\to \mathcal Y$ is Fr\'{e}chet differentiable in a neighborhood $\Omega$ of a point $\bar{x}$ in $\mathcal X$, $g:\Omega\subseteq \mathcal X\to \mathcal Y$ is linear and differentiable at a point $\bar{x}$, and $\mathcal F$ is a set-valued mapping with closed graph acting in Banach spaces $\mathcal X$ and $\mathcal Y$. Semilocal and local convergence of the extended Newton-type method are analyzed.

scholarly journals On the Local Convergence of Regula-falsi-type Method for Generalized Equations

2017 ◽  
Vol 2 (3) ◽  
Author(s):  
Farhana Alam ◽  
◽  
M. H. Rashid ◽  
M. A. Alom ◽  
◽  
...  
Keyword(s):  
Local Convergence ◽  
Generalized Equations ◽  
Type Method

scholarly journals Convergence of the Newton-Type Method for Generalized Equations

2016 ◽  
Vol 35 ◽  
pp. 27-40 ◽  
Author(s):  
MH Rashid ◽  
A Sarder
Keyword(s):  
Banach Spaces ◽  
Differentiable Function ◽  
Local Convergence ◽  
Generalized Equation ◽  
Generalized Equations ◽  
Closed Graph ◽  
Type Method ◽  
Set Valued Mapping ◽  
Fréchet Differentiable

Let X and Y be real or complex Banach spaces. Suppose that f: X->Y is a Frechet differentiable function and F: X => 2Yis a set-valued mapping with closed graph. In the present paper, we study the Newton-type method for solving generalized equation 0 ? f(x) + F(x). We prove the existence of the sequence generated by the Newton-type method and establish local convergence of the sequence generated by this method for generalized equation.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 27-40

scholarly journals Jacobian Nonsingularity in Nonlinear Symmetric Conic Programming Problems and Its Application

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yun Wang ◽  
Dezhou Kong
Keyword(s):  
Sequential Quadratic Programming ◽  
Conic Programming ◽  
Quadratic Term ◽  
Sufficient Condition ◽  
Sufficient Optimality Condition ◽  
Convergence Properties ◽  
Linear Quadratic ◽  
Generalized Jacobian ◽  
Type Method ◽  
Clarke’S Generalized Jacobian

This paper considers the nonlinear symmetric conic programming (NSCP) problems. Firstly, a type of strong sufficient optimality condition for NSCP problems in terms of a linear-quadratic term is introduced. Then, a sufficient condition of the nonsingularity of Clarke’s generalized Jacobian of the Karush–Kuhn–Tucker (KKT) system is demonstrated. At last, as an application, this property is used to obtain the local convergence properties of a sequential quadratic programming- (SQP-) type method.

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