TITLE:
Solving Smooth Generalized Equations Using Modified Gauss-Type Proximal Point Method
AUTHORS:
Md. Asraful Alom, Md. Bayezid Gazi, Imran Hossain, Eshita Kundu
KEYWORDS:
Set-Valued Mapping, Metrically Regular Mapping, Smooth Function, Lipschitz-Like Mapping, Semi-Local Convergence
JOURNAL NAME:
Applied Mathematics,
Vol.13 No.6,
June
22,
2022
ABSTRACT: Consider X and Y are two real or complex Banach spaces. We introduce and study a modified Gauss-type proximal point algorithm (in short modified G-PPA) for solving the generalized equations of the form 0 ∈ h(x) + H(x), where h :X→Y is a smooth function on Ω ⊆ X and H : X ⇉ 2Y is a set valued mapping with closed graph. When H is metrically regular and under some sufficient conditions, we analyze both semi-local and local convergence of the modified G-PPA. Moreover, the convergence results of the modified G-PPA are justified by presenting a numerical example.