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所在平台: Udemy |
课程主页: https://www.udemy.com/course/linear-programming-basics/
课程评论：没有评论
**课程名称：** 线性规划基础 (Linear Programming basics) **课程概述：** 本课程深入探讨线性规划这一在数据科学、工程、交通、供应链等众多领域广泛应用的优化工具。线性规划不仅本身具有重要价值，更是混合整数线性规划 (MILP) 和列生成等复杂优化工具的基础。 课程内容结构清晰，主要包括以下四个部分： 1. **线性规划导论：** 介绍线性规划的基本概念，并探索凸集与最优性等理论知识。 2. **求解线性规划：** 在建立基础理论之后，学习使用单纯形法 (simplex method) 求解线性规划。 3. **线性规划对偶性：** 深入理解对偶性概念，包括强对偶性 (strong duality)，互补松弛性 (complementary slackness) 和 Farkas 引理。课程将用易于理解的方式讲解这些相对复杂的概念，帮助学习者为最小化问题获得下界，并提供最优性或不可行性的证明。 4. **敏感性分析：** 探索在调整线性规划模型参数时，对模型解的影响。 **学习要点：** * 掌握线性规划的基础理论，包括凸集和最优性。 * 熟练运用单纯形法解决线性规划问题。 * 理解并应用线性规划的对偶性理论，包括强对偶性、互补松弛性和 Farkas 引理。 * 学会进行敏感性分析，评估模型参数变化对结果的影响。 **先修要求：** * 具备基础的线性代数知识，有助于理解证明部分。 **课程特色：** * 每章节后均设有练习题，帮助巩固和评估学习效果。 * 讲师积极鼓励学生提问，并提供答疑和每周一次的线下答疑时间（先到先得）。 **请注意：** 本课程主要侧重于线性规划的理论和求解方法，较少涉及建模问题，建模部分是另一门独立课程的内容。
Linear programming is a widely used optimization tool in various applications (data science, engineering, transportation, supply chain, etc.). Linear programming also makes the basic foundation behind complex optimization tools like Mixed Integer Linear Programming (MILP) and Column generation. In this course, we will study the basic theoretical concepts related to linear programming. The course is organized as follows. In the first section, we will introduce linear programming, and we will explore the convexity and types of optimalities. Then, in the second section, we will build up on the basics to learn ways to solve the linear program using the simplex method. We will then explore the concept of linear programming duality. We will also go through some of the hardest-to-understand concepts like strong duality, complementary slackness, and Farkas' lemma. Furthermore, we try to understand these concepts in an easy-to-follow way. This allows one to obtain lower bounds on the minimization problem and provide proof of optimality or Infeasibility. In the last section, we will explore how to perform sensitivity analysis (the effects of changing parts of a linear program). At the end of each section, there are assignments to help you evaluate your knowledge.As you would have noticed, this course doesn't explore modeling optimization problems as a linear program much. That is a separate topic and deserves an entire course on it. A background in basic linear algebra is needed to understand the proofs. In case you face trouble with any of the lectures or assignments, feel free to reach out to me. I am always eager to help students. You can also schedule office hours from my website once a week (first come, first served) to clear your doubts.
