Splitting Algorithm for Solving Mixed Variational Inequalities with Inversely Strongly Monotone Operators

We consider a boundary value problem whose generalized statement is formulated as a mixed variational inequality in a Hilbert space. The operator of this variational inequality is a sum of several inversely strongly monotone operators (which are not necessarily potential operators). The functional o...

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Bibliographic Details
Published inMatrix Methods: Theory, Algorithms And Applications pp. 416 - 432
Main Authors Badriev, Ildar, Zadvornov, Oleg
Format Book Chapter
LanguageEnglish
Published WORLD SCIENTIFIC 01.04.2010
Subjects
Matrices and Applications
inversely strongly monotone operator
iterative method
variational inequality
Online AccessGet full text
ISBN9812836020
9789812836014
9812836012
9814469556
9789812836021
9789814469555
DOI10.1142/9789812836021_0027

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Summary:We consider a boundary value problem whose generalized statement is formulated as a mixed variational inequality in a Hilbert space. The operator of this variational inequality is a sum of several inversely strongly monotone operators (which are not necessarily potential operators). The functional occurring in this variational inequality is also a sum of several lower semi-continuous convex proper functionals. For solving of the considered variational inequality a decomposition iterative method is offered. The suggested method does not require the inversion of original operators. The convergence of this method is investigated.
ISBN:9812836020
9789812836014
9812836012
9814469556
9789812836021
9789814469555
DOI:10.1142/9789812836021_0027