Abstract
Minty variational inequalities are considered as related to the scalar minimization problem in which the objective function is a primitive of the operator involved in the inequality itself. Well-posedness (in the sense of Tykhonov) of this primitive problem is proved as a consequence of the existence of a strict solution of a Minty variational inequality.Further, the vector extension of Minty variational inequality proposed by F. Giannessi is considered. We observe that, in this case, the relationships with the primitive vector optimization problem extend those known for the scalar case only under convexity hypotheses. A notion of solution of a Minty vector inequality, stronger than that introduced by Giannessi, is presented to fulfill this gap.KeywordsMinty variational inequalitiesvector variational inequalitiesvector optimizationwell-posedness
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