整数线性规划和线性规划的约束原理
[英]Bound Principle for Integer Linear Programming and Linear Programming
问题描述
Currently, I am learning approximation algorithms. 
目前，我正在学习近似算法。 When I learned Vertex Cover via LP, I encountered a principle called Bounding Principles. 通过LP学习“顶点覆盖”时，我遇到了一个称为“边界原理”的原理。 It like this: 像这样：
(1) The maximum value for an ILP problem is always less than or equal to the maximum value for the LP relaxation: （1）ILP问题的最大值始终小于或等于LP松弛的最大值：
MAX for ILP ≤ MAX for LP relaxation ILP的MAX≤LP松弛的MAX
(2) The minimum value for an ILP problem is always greater than or equal to the minimum for the LP relaxation: （2）ILP问题的最小值始终大于或等于LP松弛的最小值：
MIN for ILP ≥ MIN for LP relaxation ILP的MIN≥LP松弛的MIN
I cannot figure out why "MAX for ILP ≤ MAX for LP relaxation" and "MIN for ILP ≥ MIN for LP relaxation". 我无法弄清楚为什么“ ILP的MAX≤LP松弛的MAX”和“ ILP的MIN≥LP松弛的MIN”。
Can anyone explain, thx! 谁能解释，谢谢！
1 个解决方案
解决方案1
1 已采纳 2013-11-12 05:34:35
An ILP has an extra constraint than LP problem. ILP比LP问题具有更多的约束。 The constraint is that all variables should be integers. 约束是所有变量都应为整数。
Hence, the optimal solution for an ILP shall be at best as good as an optimal solution for an LP problem, it can never be better. 因此，ILP的最佳解决方案最好与LP问题的最佳解决方案一样好，再好不过了。
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