SIAM Journal on Control and Optimization · 2000 · 75 citations · 32 references
Natural SciencesComputational EngineeringFinite Element AnalysisFinite Element MethodsOptimizationConvergence AnalysisConvex AnalysisOperator TheoryVariational FormulationVariational InequalitiesWeak ConvergenceConvex Variational ProblemsFinite-dimensional Hilbert SpacesGeneralized Variational InequalitiesProximal AlgorithmsVariational Inequality Existence TheoremsVariational Inequality ProblemsVariational Inequality TheoryVariational Problems
In this paper we prove well-definedness and weak convergence of the generalized proximal point method when applied to the variational inequality problem in reflexive Banach spaces. The proximal version we consider makes use of Bregman functions, whose original definition for finite dimensional spaces has here been properly extended to our more general framework.
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