Generalizations of Farkas’ Theorem
B. D. Craven, J. J. Koliha · SIAM Journal on Mathematical Analysis · 1977
A unified treatment is given of generalizations of Farkas’ theorem on linear inequalities to arbitrary convex cones and to dual pairs of real vector spaces of arbitrary dimension. Various theorems for locally convex spaces readily follow. The results are applied to duality and converse duality theory for linear programming and to a generalization of the Kuhn–Tucker theorem, both of these in spaces of arbitrary dimension and with inequalities involving arbitrary convex cones.