Metric subregularity for composite-convex generalized equations in Banach spaces

2011 ◽  
Vol 74 (10) ◽  
pp. 3311-3323 ◽  
Author(s):  
Xi Yin Zheng ◽  
Wei Ouyang
Keyword(s):  
Banach Spaces ◽  
Generalized Equations ◽  
Metric Subregularity

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 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

Hölder metric subregularity for multifunctions in type Banach spaces

Optimization ◽  
2016 ◽  
Vol 65 (11) ◽  
pp. 1963-1982 ◽  
Author(s):  
Binbin Zhang ◽  
Kung-Fu Ng ◽  
Xi Yin Zheng ◽  
Qinghai He
Keyword(s):  
Banach Spaces ◽  
Metric Subregularity ◽  
Hölder Metric ◽  
Hölder Metric Subregularity

scholarly journals Metric Subregularity for Subsmooth Generalized Constraint Equations in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
He Qinghai ◽  
Yang Ji ◽  
Zhang Binbin
Keyword(s):  
Banach Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Normal Cones ◽  
Metric Subregularity ◽  
Constraint Equations ◽  
Asplund Spaces ◽  
Necessary And Sufficient ◽  
Generalized Constraint

This paper is devoted to metric subregularity of a kind of generalized constraint equations. In particular, in terms of coderivatives and normal cones, we provide some necessary and sufficient conditions for subsmooth generalized constraint equations to be metrically subregular and strongly metrically subregular in general Banach spaces and Asplund spaces, respectively.

Sign in / Sign up

Export Citation Format

Share Document