David Bartl (Department of Informatics and Mathematics, School of Business Administration in Karviná, Silesian University in Opava): A discrete variant of Farkas' Lemma, some related results, and homogeneous linear programming

The talk will present a discrete variant of Farkas' Lemma in the setting of a module over a linearly ordered commutative ring (such as the ring of the integer numbers, i.e. the discrete case; apart from the setting of a vector space over a linearly ordered field, which could be the continuous case).  We shall then present the corresponding discrete variants of some related results:  Tucker's Key Theorem, Motzkin's Theorem and Tucker's Theorem.  Finally, we shall discuss a possible application of the discrete variant of Farkas' Lemma in the duality theory of linear programming.  We shall introduce the concept of the homogeneous linear program, its dual problem, and mention that the strong duality holds.