The purpose of this paper is twofold; first, to present a simple proof of the Farkas theorem (or Farkas lemma or Farkas-Minkowski lemma), proof performed through a nonlinear theorem of the alternative; second, to present various new proofs of the so-called "Tucker key theorem", and to show that...

We give an overview and make some remarks on the approximate optimality conditions, for a nonlinear programming problem, given by Haeser and Schuverdt (2011) and by Fiacco and McCormick (1968a). Other first-order optimality conditions in absence of constraint qualifications are examined....

In this paper we take in to considerations some classes of matrices which are generalizations of the class of K-matrices, in the terminology of Fielder and Ptàk (1962). We study the hierarchy and inclusion relations between the classes considered and we point out some economic applications

La presente nota, di intenti prevalentemente didattici, prende lo spunto dal corso di Economia Matematica tenuto dal primo degli autori presso il Dipartimento di Scienze Eco- nomiche e Aziendali dell'?Università di Pavia. Ci proponiamo, infatti, di appianare alcune difficoltà relative alla...

We give an overview of constraint qualifications and optimality conditions for a nonlinear pro- gramming problems where the functions involved have directional derivatives defined in an axiomatic way. We consider mainly the approach of Elster and Thierfelder (1985, 1988a, 1988b) and the approach...

Si prendono in considerazione i legami esistenti tra i problemi "classici" di programmazione matematica, con vincoli espressi da uguaglianze, ed i problemi "moderni" di ottimo vincolato, ossia i problemi di programmazione matematica con vincoli espressi da disuguaglianze.

We give an overview on the main properties of D-stable matrices, i.e. of those square matrices $A$ for which the product DA is stable for any choice of the diagonal matrix D, with all positive diagonal elements. These matrices, introduced in economic analysis by Arrow and Mc Manus (1958), have...