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Michele Conforti (confortimath.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 (lexcut) that eliminates the integer points in B that are lexicographically smaller than x and is satisfied by the others. The family of lexcuts contains the ChvatalGomory 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 worstcase 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 ) Citation: Download: [PDF] Entry Submitted: 07/25/2018 Modify/Update this entry  
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