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

Del Prete, Imma; Lignola, M. Beatrice; Morgan, Jacqueline

JIPAM, J. Inequal. Pure Appl. Math. 4, No. 1, Paper No. 5, 18 p. (2003).

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.

Reviewer: Nicolas Hadjisavvas (Hermoupolis)

MSC:

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

Keywords:

variational inequalities; maximum problems; well-posedness