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A direct splitting method for nonsmooth variational inequalities
journal contribution
posted on 2014-06-01, 00:00 authored by J Y Bello Cruz, Reinier Diaz MillanReinier Diaz MillanWe propose a direct splitting method for solving a nonsmooth variational inequality in Hilbert spaces. The weak convergence is established when the operator is the sum of two point-to-set and monotone operators. The proposed method is a natural extension of the incremental subgradient method for nondifferentiable optimization, which strongly explores the structure of the operator using projected subgradient-like techniques. The advantage of our method is that any nontrivial subproblem must be solved, like the evaluation of the resolvent operator. The necessity to compute proximal iterations is the main difficulty of other schemes for solving this kind of problem.
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Journal
Journal of optimization theory and applicationsVolume
161Issue
3Pagination
728 - 737Publisher
SpringerLocation
New York, N.Y.Publisher DOI
ISSN
0022-3239eISSN
1573-2878Language
EnglishPublication classification
C1.1 Refereed article in a scholarly journalUsage metrics
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No categories selectedKeywords
Science & TechnologyTechnologyPhysical SciencesOperations Research & Management ScienceMathematics, AppliedMathematicsMaximal monotone operatorsMonotone variational inequalitiesProjection methodsSplitting methodsMONOTONE-OPERATORSPROJECTION METHODPROXIMAL METHODSHILBERT-SPACESALGORITHMCONVERGENCEOPTIMIZATIONSUM
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