TITLE:
Convergence Analysis of General Version of Gauss-Type Proximal Point Method for Metrically Regular Mappings
AUTHORS:
Md. Asraful Alom, Mohammed Harunor Rashid, Kalyan Kumer Dey
KEYWORDS:
Set-Valued Mappings, Metrically Regular Mappings, Lipschitz-Like Mapping, Local and Semi-Local Convergence
JOURNAL NAME:
Applied Mathematics,
Vol.7 No.11,
July
20,
2016
ABSTRACT: We introduce and study in the present paper
the general version of Gauss-type proximal point algorithm (in short GG-PPA)
for solving the inclusion , where T is a set-valued mapping which is not
necessarily monotone acting from a Banach space X to a subset of a Banach space
Y with locally closed graph. The convergence of the GG-PPA is present here by
choosing a sequence of functions with , which is Lipschitz continuous in a
neighbourhood O of the origin and when T is metrically regular. More precisely,
semi-local and local convergence of GG-PPA are analyzed. Moreover, we present a
numerical example to validate the convergence result of GG-PPA.