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New concepts of well-posedness for optimization problems with variational inequality constraints. (English) Zbl 1029.49024

In this paper various concepts of well-posedness are introduced and studied for families of variational inequalities, indexed over a topological space. Conditions ensuring well-posedness are given. In the special case where the variational inequalities stem from a family of optimization problems, well-posedness for the variational inequalities is compared to well-posedness of the optimization problems.

MSC:

49K40 Sensitivity, stability, well-posedness
49J40 Variational inequalities
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