An explicit algorithm for monotone variational inequalities

We introduce a fully explicit method for solving monotone variational inequalities in Hilbert spaces, where orthogonal projections onto the feasible set are replaced by projections onto suitable hyperplanes. We prove weak convergence of the whole generated sequence to a solution of the problem, unde...

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Bibliographic Details
Published inOptimization Vol. 61; no. 7; pp. 855 - 871
Main Authors Cruz, J.Y. Bello, Iusem, A.N.
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis Group 01.07.2012
Taylor & Francis LLC
Subjects
Algorithms
Continuity
Convergence
Euclidean space
Hyperplanes
Inequalities
Mathematical problems
maximal monotone operators
monotone variational inequalities
Operators
Optimization
Optimization algorithms
Projection
projection method
relaxed method
Studies
weak convergence
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Summary:We introduce a fully explicit method for solving monotone variational inequalities in Hilbert spaces, where orthogonal projections onto the feasible set are replaced by projections onto suitable hyperplanes. We prove weak convergence of the whole generated sequence to a solution of the problem, under only the assumptions of continuity and monotonicity of the operator and existence of solutions.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2010.536232