Nonlinear Analysis 63 (2005) e1655 – e1664 www.elsevier.com/locate/na Duality theory and optimality conditions for Generalized Complementarity Problems S. Giuffrè a , ∗ , G. Idone a , A. Maugeri b a D.I.M.E.T. Faculty of Engineering, University of Reggio Calabria, via Graziella, Loc. Feo diVito, 89060 Reggio Calabria, Italy b Department of Mathematics and Computer Science, University of Catania, Viale A. Doria, 6, 95125 Catania, Italy Abstract In this paper Generalized Complementarity Problems are expressed in terms of suitable optimization problems and some necessary optimality conditions are given. The infinite dimensional Lagrangean and Duality Theories play an important role in order to achieve the main results.  2005 Elsevier Ltd. All rights reserved. Keywords: Generalized complementarity problem; Lagrangean function; Dual problem; Quasi-relative interior; Saddle point 1. Introduction Let S be a nonempty subset of a real linear space X. Let Y be a partially ordered real normed space with the ordering cone C. Let Z be the set of nonnegative measurable functions and let L : S → Z, B : S → Z be two operators. Let g : S → Y be a given constraint mapping and let us set K ={v ∈ S : g(v) ∈-C}. (1) ∗ Corresponding author. E-mail address: sofia.giuffre@unirc.it (S. Giuffrè). 0362-546X/$ - see front matter  2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.na.2004.12.019