2023-09-16 复习LP

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一些对过去学习的Linear Programming知识的回顾(通过做习题)


先列出所有过去的笔记:

(在此之前还有一篇(🔗 [MIT 6.251J Introduction To Mathematical Programming前置知识学习(2023-06-16) - Truxton's blog] https://truxton2blog.com/2024-06-16-learn-mit-intro-to-mathematical-programming/),但学偏了,不列了)

(从完全不懂LP到simplex algorithm的一堆混乱笔记)🔗 [(2023年6月)Introduction to Linear Optimization学习笔记1 - Truxton's blog] https://truxton2blog.com/2023-06-intro-to-linear-optimization-learning-notes-1/

(Chapter 1习题)凸集相关的证明,简单的LP列公式场景题:🔗 [MIT 6.251J Introduction To Mathematical Programming学习(2023-07-06,Assignment 1的相关笔记) - Truxton's blog] https://truxton2blog.com/2023-07-06-intro-to-mathematical-programming-assignment-1-learning-notes/

(Chapter 2习题)多胞体,极点等几何空间:🔗 [MIT 6.251J Introduction To Mathematical Programming学习(2023-07-14,Assignment 2的相关笔记) - Truxton's blog] https://truxton2blog.com/2023-07-14-intro-to-mathematical-programming-assignment-2-learning-notes/

(Chapter 3习题)simplex algorithm的一些简单习题:🔗 [MIT 6.251J Introduction To Mathematical Programming学习(2023-07-14,Assignment 3的相关笔记) - Truxton's blog] https://truxton2blog.com/2023-07-14-intro-to-mathematical-programming-assignment-3-learning-notes/


需要补充:

带有绝对值符号,且分多种情况的LP问题如何正确化简(或者写成规范形式)

原题:

🔗 [optimization - Minimized sum of the distances with street distance - Mathematics Stack Exchange] https://math.stackexchange.com/questions/692675/minimized-sum-of-the-distances-with-street-distance

参考:

(未必正确)🔗 [optimization - Linear programming: minimizing absolute values and formulate in LP - Mathematics Stack Exchange] https://math.stackexchange.com/questions/1954992/linear-programming-minimizing-absolute-values-and-formulate-in-lp

关于绝对值符号,还可以参考之前的一道题:p=12353


补充了LP问题的standard format和canonical format(标准型和规范型)

补充在p=12129

忘记怎么对付无约束变量了,所以回顾了p12129的这张图

此外还有min()和max()之间的转换(不一定需要是standard/canonical form):

🔗 [optimization - How to convert a minimization problem to maximization problem and vice versa - Mathematics Stack Exchange] https://math.stackexchange.com/questions/3274989/how-to-convert-a-minimization-problem-to-maximization-problem-and-vice-versa


汉堡店问题(雇佣员工,同时要求每名员工一周连续工作任意5天),以及一个变种的汉堡店问题(允许兼职工/短工)

原题忘了,等找到类似的再补充回来

过了一年终于补充回来了:🔗 [LP建模问题:汉堡店雇佣员工 - Truxton's blog] https://truxton2blog.com/lp-workforce-scheduling-problem/


当前习惯使用的那个latex LP表达式有的时候并不好看,可能需要调整一下

后续:chatgpt帮我修好了


好像没有什么难题了


以后有机会学一下LP and Game



 Last Modified in 2025-07-14 

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