Lexicographic linear programming, Duality Theorem, Simplex method, Farkas' Lemma.

We formulate the primal and dual problem of lexicographic linear programming in an infinite-dimensional real vector space. Mentioning the lexicographic version of Farkas' Lemma, we can prove the Duality Theorem for those two formulated problems. We also describe a generalised simplex method which can solve the problems of lexicographic linear programming in infinite-dimensional spaces. If the objective function of the primal problem is chosen appropriately, degeneracy can be avoided: finiteness of the simplex method is ensured thus.