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Zbl 1136.49007
Bianchi, M.; Hadjisavvas, N.; Schaible, S.
Exceptional families of elements for variational inequalities in Banach spaces. (English)
[J] J. Optim. Theory Appl. 129, No. 1, 23-31 (2006). ISSN 0022-3239; ISSN 1573-2878/e

Summary: In keeping with very recent efforts to establish a useful concept of an exceptional family of elements for variational inequality problems rather than complementarity problems as in the past, we propose such a concept. It generalizes previous ones to multivalued variational inequalities in general normed spaces and allows us to obtain several existence results for variational inequalities corresponding to earlier ones for complementarity problems. Compared with the existing literature, we consider problems in more general spaces and under considerably weaker assumptions on the defining map.

MSC 2000:: *49J40 Variational methods including variational inequalities
47J20 Inequalities involving nonlinear operators

Keywords: variational inequalities; complementarity problems; quasimonotone maps; exceptional families of elements

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Zentralblatt MATH Berlin [Germany]