Mar 18, 2021 · Theorem 6 (Integer Farkas Lemma). Let Ax = b be a rational linear system. There exists an integral solution x satisfying Ax = b iff yT b is an ...
Farkas' lemma is a solvability theorem for a finite system of linear inequalities. It was originally proven by the Hungarian mathematician Gyula Farkas.
Dec 1, 2022 · A lot of questions regarding the Farkas' lemma has already been done here. Most of them seems to be related to consequences of the Farkas' lemma ...
One of the central fundaments of this duality result is the so-called Farkas lemma that establishes that a given system of linear inequalities has a solution if ...
Mar 2, 2015 · Farkas type results are available for solutions to linear systems. These can also include restrictions such as nonnegative solutions or ...
Along the same lines, we also provide a discrete Farkas lemma and show that the exis- tence of a nonnegative integral solution x ∈ Nn to Ax = b can be tested.
Mar 16, 2023 · Theorem 6.3 (Integer Farkas Lemma). Let A ∈ Qm×d and b ∈ Qm. The system Ax = b, x ∈ Zd is infeasible if and only if there exists a vector u ...
It is a fundamental result in the theory of integer optimization that one can give a certificate for a vector not being a member of a lattice. This result can.
Farkas type results are available for solutions to linear systems. These can also include restrictions such as nonnegative solutions or integer solutions.
Farkas' Lemma is a foundational result in linear programming, with implications in duality, optimality conditions, and stochastic and bilevel programming.