GENERAL GAUSS-TYPE PROXIMAL POINT METHOD AND ITS CONVERGENCE ANALYSIS FOR SMOOTH GENERALIZED EQUATIONS

Full Article - PDF

Published: 2017-03-02

Page: 296-310


MD. ASRAFUL ALOM

Department of Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh. and Department of Mathematics, Khulna University of Engineering and Technology, Khulna-9203, Bangladesh.

MOHAMMED HARUNOR RASHID *

Department of Mathematics, University of Rajshahi, Rajshahi-6205, Bangladesh.

*Author to whom correspondence should be addressed.


Abstract

Let X and Y be Banach spaces and Ω be an open subset of X. In the present paper, a general Gauss-type Proximal Point Algorithm (GGPPA) is introduced for approximating the solution of a generalized equation  0∈f(x)+F(x),  where f:X→ Y is a differentiable function on Ω and F:X⇉2^Y is a set valued mapping with closed graph. Semilocal and local convergences of the GGPPA are presented by considering a sequence of Lipschitz continuous functions gk:X→ Y such that gk (0)=0 around the origin with positive Lipschitz constants λk and the metric regularity condition of F. Finally, we give a numerical example to verify the convergence results of the GGPPA.

Keywords: Generalized equations, set-valued mapping, Metrically regular mapping, Lipschitz-like mapping, semi-local convergence


How to Cite

ALOM, M. A., & RASHID, M. H. (2017). GENERAL GAUSS-TYPE PROXIMAL POINT METHOD AND ITS CONVERGENCE ANALYSIS FOR SMOOTH GENERALIZED EQUATIONS. Asian Journal of Mathematics and Computer Research, 15(4), 296–310. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/802

Downloads

Download data is not yet available.