ABSTRACT
In the first section of this chapter, the authors present the main results of the theory of pseudo-monotone and generalized pseudo-monotone multivalued mappings developed by Browder and Hess. The notion of pseudo-monotone operators first given in [Brez68] has been applied to the treatment of multivalued mappings in [Bro72] and [Bro75]. The second section is devoted to the study of some general properties of functions having pseudo-monotone and generalized pseudo-monotone generalized gradients. Finally the notion of quasi-pseudo-monotonity is introduced and corresponding propositions are proved. Two classes of functions will be considered: the first class includes locally Lipschitz functions while the second one includes indicator functions of some nonconvex closed sets. Finally the notion of quasi-pseudo-monotonity is introduced and corresponding propositions are proved.
