On Disjunction Convex Hulls by Lifting

被引：1

作者：

Qu, Yushan ^{[1
]}

Lee, Jon ^{[1
]}

机构：

[1] Univ Michigan, Ann Arbor, MI 48109 USA

来源：

COMBINATORIAL OPTIMIZATION, ISCO 2024 | 2024年 / 14594卷

基金：

美国国家科学基金会;

关键词：

mixed-integer optimization; disjunction; big M; lifting; convex hull; facet;

D O I：

10.1007/978-3-031-60924-4_1

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

We study the natural extended-variable formulation for the disjunction of n+1 polytopes in R-d. We demonstrate that the convex hull D in the natural extended-variable space Rd+n is given by full optimal big-M lifting (i) when d <= 2 (and that it is not generally true for d >= 3), and also (ii) when the polytopes are all axis-aligned hyper-rectangles. We give further results on the polyhedral structure of D, emphasizing the role of full optimal big-M lifting.

引用

页码：3 / 15

页数：13

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