A Short Algebraic Proof of the Farkas Lemma

DOI10.1137/06067438zbMath1158.15015OpenAlexW2093266057WikidataQ124883796 ScholiaQ124883796MaRDI QIDQ3608980

David Bartl

Publication date: 6 March 2009

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/06067438

zbMATH Keywords

systems of linear inequalitiestheorems of the alternativeFarkas lemmaMotzkin's theoremTucker's theoremlinearly ordered vector spaces

Mathematics Subject Classification ID

Linear inequalities of matrices (15A39) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Ordered fields (12J15)

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Subdifferential stability analysis for convex optimization problems via multiplier sets ⋮ Affine variational inequalities on normed spaces ⋮ The Farkas Lemma revisited ⋮ A very short algebraic proof of the Farkas lemma ⋮ Nonlinear perturbations of polyhedral normal cone mappings and affine variational inequalities ⋮ Separation theorems for convex polytopes and finitely-generated cones derived from theorems of the alternative ⋮ Linearly perturbed polyhedral normal cone mappings and applications ⋮ A discrete variant of Farkas' lemma ⋮ A discrete variant of Farkas' lemma and related results ⋮ Differential stability of convex discrete optimal control problems ⋮ New results on linearly perturbed polyhedral normal cone mappings ⋮ Differential stability of convex optimization problems under inclusion constraints ⋮ Coderivatives of normal cone mappings and Lipschitzian stability of parametric variational inequalities ⋮ Linearly perturbed generalized polyhedral normal cone mappings and applications ⋮ A note on the short algebraic proof of Farkas' Lemma ⋮ Comments on: ``Farkas' lemma: three decades of generalizations for mathematical optimization ⋮ New approach to Farkas' theorem of the alternative

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