Duality and a Farkas lemma for integer programs

Jean B. Lasserre ()
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Jean B. Lasserre: LAAS-CNRS

Chapter Chapter 2 in Optimization, 2009, pp 15-39 from Springer

Abstract: Abstract We consider the integer program $$\max \{c x\,|\,Ax=b,x \in {\bf N}^n\}$$ . A formal parallel between linear programming and continuous integration, and discrete summation, shows that a natural duality for integer programs can be derived from the $${\bf Z}$$ -transform and Brion and Vergne’s counting formula. Along the same lines, we also provide a discrete Farkas lemma and show that the existence of a nonnegative integral solution $$x\in{\bf N}^n$$ to $$Ax=b$$ can be tested via a linear program.

Keywords: Integer programming; counting problems; duality (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-0-387-98096-6_2

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DOI: 10.1007/978-0-387-98096-6_2

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