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Pseudomonotone complementarity problems and variational inequalities. (English) Zbl 1106.49020

Hadjisavvas, Nicolas (ed.) et al., Handbook of generalized convexity and generalized monotonicity. New York, NY: Springer (ISBN 0-387-23255-9/hbk). Nonconvex Optimization and its Applications 76, 501-558 (2005).
Complementarity problems and variational inequality problems are closely related although their developments have followed quite different paths. The main distinction is the space setting in which these two problems were considered. Variational inequality problems were usually studied in infinite-dimensional metric spaces while complementarity problems in finite-dimensional Euclidean spaces.
In this chapter, the authors present a survey of the recent results on existence and uniqueness of solutions for both problems in infinite-dimensional spaces under pseudomonotonicity assumptions. Applications to optimization problems and, in particular, to least element problems are given to illustrate the general theory.
For the entire collection see [Zbl 1070.26002].

MSC:

49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
47H04 Set-valued operators
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