An iterative regularization method for variational inequalities in Hilbert spaces-Reference-Cited by-同舟云学术

An iterative regularization method for variational inequalities in Hilbert spaces

Published:2020-09-30 Issue:3 Volume:36 Page:475-482
ISSN:1843-4401
Container-title:Carpathian Journal of Mathematics
language:
Short-container-title:CJM

Author:

XU HONG-KUN¹,ALTWAIJRY NAJLA²,CHEBBI SOUHAIL³

Affiliation:

1. DEPARTMENT OF MATHEMATICS HANGZHOU DIANZI UNIVERSITY SCHOOL OF SCIENCE HANGZHOU 310018, CHINA E-mail address: xuhk@hdu.edu.cn

2. DEPARTMENT OF MATHEMATICS KING SAUD UNIVERSITY COLLEGE OF SCIENCE P.O. BOX 2455, RIYADH 11451, SAUDI ARABIA E-mail address: najla@ksu.edu.sa

3. DEPARTMENT OF MATHEMATICS KING SAUD UNIVERSITY COLLEGE OF SCIENCE P.O. BOX 2455, RIYADH 11451, SAUDI ARABIA E-mail address: schebbi@ksu.edu.sa

Abstract

We consider an iterative method for regularization of a variational inequality (VI) defined by a Lipschitz continuous monotone operator in the case where the set of feasible solutions is decomposed to the intersection of finitely many closed convex subsets of a Hilbert space. We prove the strong convergence of the sequence generated by our algorithm. It seems that this is the first time in the literature to handle iterative solution of ill-posed VIs in the domain decomposition case.

Publisher

Technical University of Cluj Napoca, North University Center of Baia Mare

Subject

General Mathematics

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