Abstract
The aim of this paper is to establish the existence of essentially connected components for Hartman-Stampacchia type variational inequalities for both set-valued and single-valued mappings in normed spaces. Our results show that each variational inequality problem has, at least, one connected component of its solutions which is stable though in general its solution set may not have a good behavior (i.e., not stable). Thus if a variational inequality problem has only one connected solution set, it must be stable. Here we don’t need to require the objective mapping to be either Lipschitz or differential.
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Isac, G., Yuan, G.XZ. (2000). The Existence of Essentially Connected Components of Solutions for Variational Inequalities. In: Giannessi, F. (eds) Vector Variational Inequalities and Vector Equilibria. Nonconvex Optimization and Its Applications, vol 38. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0299-5_14
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DOI: https://doi.org/10.1007/978-1-4613-0299-5_14
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