Università degli Studi di Salerno · 2007 · 14 citations · 8 references
Natural SciencesMathematicsDesign OptimizationDifferential EquationsOptimizationConstrained OptimizationConvex AnalysisOptimization TheoryVariational FormulationVariational InequalitiesVariational OptimizationExistence Of MinimizersMinty Variational InequalitiesOptimality ConditionsSubject ClassificationVariational Inequality ProblemsVariational Inequality TheoryVariational Problems
In this paper we survey the relationships between scalar and vector variational inequalities (of differential type) and the underlying optimization problem. We show that the variational inequalities of Stampacchia type can be viewed as necessary optimality conditions, while the variational inequalities of Minty type can be considered as sufficient optimality conditions. Concerning this last statement, a gap is observed between the scalar and the vector case and possible fulfilments of this gap are investigated. Mathematics Subject Classification: 65K10 49J40 58E35
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