Catálogo de publicaciones - libros

This chapter is an introduction to generalized monotone multivalued maps and their relation to generalized convex functions through subdifferential theory. In particular, it contains the characterization of various types of generalized convex functions through properties of their subdifferentials. Also, some recent results on properly quasimonotone maps, maximal pseudomonotone maps, and a new “quasiconvex” subdifferential are presented.

In this chapter, we report recent results mainly on existence for complementarity problems and variational inequalities in infinite-dimensional spaces under generalized monotonicity, especially (algebraic) pseudomonotonicity. Variational inequalities associated to a topological pseudomonotone operator have been also considered and some possible extensions of complementarity problems and variational inequalities have been included. Finally some discussions on the equivalence of complementarity problems for pseudomonotone operators are given.

This chapter is devoted to equilibrium problems and variational inequalities under generalized monotonicity assumptions on cost functions. We present basic existence and uniqueness results of solutions both for scalar and for vector problems. Relationships between generalized monotonicity properties of cost functions of these problems are also considered. Moreover, we describe basic approaches to construct iterative solution methods, including their convergence properties.

This chapter presents some uses of generalized concavity and generalized monotonicity in consumer theory and general equilibrium theory. The first part emphasizes the relationship between generalized monotonicity properties of individual demand and axioms of revealed preference theory. The second part points out the relevance of pseudomonotone market excess demand to a well-behaved general equilibrium model. It is shown that this property can be derived from assumptions on the distribution of individual (excess) demands.