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
收藏
页码：3 / 15
页数：13
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