o Giorgi

Invexity and Optimization

Introduction.- Invex Functions (The Smooth Case).- Pseudolinearity. Invexity and Generalized Monotonicity.- Extensions of Invexity to Nondifferentiable Functions.- Invexity in Nonlinear Programming.- Invex Functions in Multiobjective Programming.- Variational and Control problems involving Invexity.- Invexity For Some Special Functions and Problems.- References.- Index.

Sensitivity analysis for variational inequalities

Abstract We investigate existence and regularity of the solution of a parametric variational inequality for small changes in the perturbation parameters. More precisely, assuming (pseudo) monotonicity of the operator, we extend a result of Kyparisis on the differentiability of the solution. Moreover, following an idea of Ralph and Dempe, we show that the solution is locally piecewise continuously differentiable, the directional derivative of the solution exists and it can be evaluated by solving a linear variational inequality.

A note on a proof of F. Hahn concerning the gross substitutability

The aim of this note is to investigate the assumptions and the proofs of some results by F. Hahn, which have been stated in several other classics of Economic Theory. The results deal with the relations between the gross substitutability and the weak axiom of revealed preference, in a pure exchange economy, ruled by the Walras law.