Farkas theorems for positively homogeneous quasiconvex functions

Abstract

The Farkas Theorem on a system of linear inequalities has been standing in the centre of interest of researchers on mathematical programming since the seminal paper of Kuhn and Tucker [12]. The truth of this claim is proved not only by the large number of citations made to the Farkas Theorem, but by the fact that a great number of its generalizations has been elaborated so far.

On the one hand the paper provides an extension of the Farkas Theorem for system of inequalities defined by positively homogeneous lower semicontinuous quasiconvex functions, while on the other hand a detailed bibliography is presented on generalizations of the Farkas Theorem.