We give an FPRAS for Holant problems with parity constraints and not-all-equal constraints,
a generalisation of the problem of counting sink-free-orientations. The approach combines a …

This paper provides new Farkas-type results characterizing the inclusion of a given set,
called contained set, into a second given set, called container set, both of them are subsets …

This book aims to provide a thorough introduction to smooth and nonsmooth (convex and
nonconvex) optimization theory on nite dimensional normed vector spaces (Rp spaces with …

Farkas established that a system of linear inequalities has a solution if and only if we cannot
obtain a contradiction by taking a linear combination of the inequalities. We state and …

We report a discrete variant of Farkas' Lemma in the setting of a module over a linearly
ordered commutative ring. The ring may contain zero divisors, and need not be associative …

We generalize Farkas' lemma to the setting of a module over a linearly ordered commutative
ring. We prove the result in full generality in a purely linear-algebraic way, without making …

This note presents a proof of the Farkas–Minkowski theorem. Our proof does not
presuppose the closedness of a finitely generated cone, nor employs separation theorems …

We study a problem of linear programming in the setting of a vector space over a linearly
ordered (possiblyskew) field. The dimension of the space may be infinite. The objective …

David Bartl1 Abstract. We have established a discrete variant of Farkas' Lemma [Bartl, D.
and Dubey, D.(2017). Operations Research Letters, 45, pp. 160–163] in the setting of a …

Bemerkung: Für eine informellere Einführung in die zentralen Ideen der vorliegenden Arbeit,
insbesondere der in Kapitel 4 und Kapitel 5 eingeführten, verweisen wir auf Kapitel 1 …