Lexicographical polytopes

Barbato, Michele; Grappe, Roland; Lacroix, Mathieu; Pira, Clément

doi:10.1016/j.dam.2017.04.022

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2018

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Cited by 2 publications

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“…The lexicographic order also applies to nonbinary vectors. Given vectors α, β ∈ Z n + , [2,4] characterize the convex hull of bounded integer vectors y satisfying α y β, where extends ≺ by allowing equality. The complete linear description has O(n) constraints, parametrized by maximal and minimal elements with respect to α and β.…”

Section: Introductionmentioning

confidence: 99%

Matrices with lexicographically-ordered rows

Angulo

2018

Optim Lett

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The lexicographic order can be used to force a collection of decision vectors to be all different, i.e., to take on different values in some coordinates. We consider the set of fixed-size matrices with bounded integer entries and rows in lexicographic order. We present a dynamic program to optimize a linear function over this set, from which we obtain a compact extended formulation for its convex hull.

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Section: Introductionmentioning

confidence: 99%

Matrices with lexicographically-ordered rows

Angulo

2018

Optim Lett

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“…For instance, box-TDI polyhedra keep their integrality after being intersected with any integer box [17]. The intersection of two polymatroids [9] or of two lexicographical polytopes [4] is integer. Calvillo characterizes the graphs whose stable set polytope remains integer after being intersected with specific hyperplanes [6].…”

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confidence: 99%