Scanning integer points with lex-inequalities: a finite cutting plane algorithm for integer programming with linear objective

Author:

Conforti Michele,De Santis MariannaORCID,Di Summa Marco,Rinaldi Francesco

Abstract

AbstractWe consider the integer points in a unimodular cone K ordered by a lexicographic rule defined by a lattice basis. To each integer point x in K we associate a family of inequalities (lex-inequalities) that define the convex hull of the integer points in K that are not lexicographically smaller than x. The family of lex-inequalities contains the Chvátal–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 $$\min \{cx: x\in S\cap \mathbb {Z}^n\}$$ min { c x : x S Z n } , where $$S\subset \mathbb {R}^n$$ S R n is a compact set and $$c\in \mathbb {Z}^n$$ c Z n . We analyze the number of iterations of our algorithm.

Funder

Ministero dell’Istruzione, dell’Università e della Ricerca

Università di Padova

Sapienza Università di Roma

Publisher

Springer Science and Business Media LLC

Subject

Computational Theory and Mathematics,Theoretical Computer Science,Management Information Systems,Management Science and Operations Research

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Binary Extended Formulations and Sequential Convexification;Mathematics of Operations Research;2023-08-24

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