Farkas-Type Results With Conjugate Functions

Abstract

We present some new Farkas-type results for inequality systems involving a finite as well as an infinite number of convex constraints. For this, we use two kinds of conjugate dual problems, namely an extended Fenchel-type dual problem and the recently introduced Fenchel--Lagrange dual problem. For the latter, which is a "combination" of the classical Fenchel and Lagrange duals, the strong duality is established.