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Scanning integer points with lex-cuts: A finite cutting plane algorithm for integer programming with linear objective

Michele Conforti (conforti***at***math.unipd.it)
Marianna De Santis (mdesantis***at***diag.uniroma1.it)
Marco Di Summa (disumma***at***math.unipd.it)
Francesco Rinaldi (rinaldi***at***math.unipd.it)

Abstract: We consider the integer points in a box B ordered by a lexicographic rule defined by a lattice basis. To each integer point x in B we associate a cutting plane (lex-cut) that eliminates the integer points in B that are lexicographically smaller than x and is satisfied by the others. The family of lex-cuts contains the Chvatal-Gomory cuts, but does not contain and is not contained in the family of split cuts. This provides a finite cutting plane method to solve the integer program min{cx: x \in S \cap Z^n}, where S \subset R^n is a compact set and c \in Z^n. We analyze the worst-case behavior of our algorithm and propose some variants.

Keywords: Integer Nonlinear Programming, Cutting plane algorithm

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Integer Programming (Cutting Plane Approaches )


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Entry Submitted: 07/25/2018
Entry Accepted: 07/25/2018
Entry Last Modified: 11/05/2018

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