Linear Inequalities


Title: Linear Inequalities
Authors: Ralph Bottesch, Alban Reynaud and René Thiemann (rene /dot/ thiemann /at/ uibk /dot/ ac /dot/ at)
Submission date: 2019-06-21
Abstract: We formalize results about linear inqualities, mainly from Schrijver's book. The main results are the proof of the fundamental theorem on linear inequalities, Farkas' lemma, Carathéodory's theorem, the Farkas-Minkowsky-Weyl theorem, the decomposition theorem of polyhedra, and Meyer's result that the integer hull of a polyhedron is a polyhedron itself. Several theorems include bounds on the appearing numbers, and in particular we provide an a-priori bound on mixed-integer solutions of linear inequalities.
  author  = {Ralph Bottesch and Alban Reynaud and René Thiemann},
  title   = {Linear Inequalities},
  journal = {Archive of Formal Proofs},
  month   = jun,
  year    = 2019,
  note    = {\url{},
            Formal proof development},
  ISSN    = {2150-914x},
License: BSD License
Depends on: LLL_Basis_Reduction
Used by: Linear_Programming