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33 个评分

孔令傑 (Ling-Chieh Kung)

4,797 人已注册

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Operations Research (2): Optimization Algorithms

国立台湾大学

课程信息

24,095 次近期查看

Operations Research (OR) is a field in which people use mathematical and engineering methods to study optimization problems in Business and Management, Economics, Computer Science, Civil Engineering, Electrical Engineering, etc.
The series of courses consists of three parts, we focus on deterministic optimization techniques, which is a major part of the field of OR.
As the second part of the series, we study some efficient algorithms for solving linear programs, integer programs, and nonlinear programs.
We also introduce the basic computer implementation of solving different programs, integer programs, and nonlinear programs and thus an example of algorithm application will be discussed.

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中级

For learners who have already taken basic operations research courses. Experience with calculus, linear algebra, and probability is suggested.

完成时间大约为12 小时

英语（English）

字幕：英语（English）

您将学到的内容有

Learn how to use algorithms to solve different types of optimization programs.

Learn how to use Gurobi solver with Python to solve these problems efficiently.

您将获得的技能

Algorithms
Business Analytics
Mathematical Optimization

可灵活调整截止日期

根据您的日程表重置截止日期。

可分享的证书

完成后获得证书

100% 在线

立即开始，按照自己的计划学习。

中级

For learners who have already taken basic operations research courses. Experience with calculus, linear algebra, and probability is suggested.

完成时间大约为12 小时

英语（English）

字幕：英语（English）

授课教师

授课教师评分

4.71/5 （14 个评分）

孔令傑 (Ling-Chieh Kung)

副教授 (Associate Professor)

資訊管理學系 (Department of Information Management)

52,846 个学生

8 门课程

提供方

国立台湾大学

We firmly believe that open access to learning is a powerful socioeconomic equalizer. NTU is especially delighted to join other world-class universities on Coursera and to offer quality university courses to the Chinese-speaking population. We hope to transform the rich rewards of learning from a limited commodity to an experience available to all.

授课大纲 - 您将从这门课程中学到什么

周

周 1

完成时间为 2 小时

Course Overview

In the first lecture, we briefly introduce the course and give a quick review about some basic knowledge of linear algebra, including Gaussian elimination, Gauss-Jordan elimination, and definition of linear independence.

完成时间为 2 小时

7 个视频（总计 73 分钟）, 1 个阅读材料, 1 个测验

7 个视频

Prelude2分钟

1-1: Overview.8分钟

1-2: The row and column views for a linear system – A two-dimensional example.5分钟

1-3: The row and column views for a linear system – A three-dimensional example.9分钟

1-4: Using Gaussian elimination to solve Ax=b – Nonsingular.24分钟

1-5: Using Gauss-Jordan elimination to solve A^(-1) – Singular.13分钟

1-6: Linear dependence and independence.9分钟

1 个阅读材料

NTU MOOC course information1分钟

1 个练习

Quiz for Week 120分钟

周

周 2

完成时间为 3 小时

The Simplex Method

Complicated linear programs were difficult to solve until Dr. George Dantzig developed the simplex method. In this week, we first introduce the standard form and the basic solutions of a linear program. With the above ideas, we focus on the simplex method and study how it efficiently solves a linear program. Finally, we discuss some properties of unbounded and infeasible problems, which can help us identify whether a problem has optimal solution.

完成时间为 3 小时

25 个视频（总计 168 分钟）

25 个视频

2-0: Opening.4分钟

2-1: Introduction.3分钟

2-2: Standard form – Extreme points.5分钟

2-3: Standard form – Standard form LPs.7分钟

2-4: Standard form – Standard form LPs in matrices.4分钟

2-5: Basic solutions – Independence among rows.6分钟

2-6: Basic solutions – Basic solutions.3分钟

2-7: Basic solutions – An example for listing basic solutions.5分钟

2-8: Basic solutions – Basic feasible solutions.8分钟

2-9: Basic solutions – Adjacent basic feasible solutions.7分钟

2-10: The simplex method – The idea.5分钟

2-11: The simplex method – The first move.12分钟

2-12: The simplex method – The second move.7分钟

2-13: The simplex method – Updating the system through elementary row operations.8分钟

2-14: The simplex method – The last attempt with no more improvement.3分钟

2-15: The simplex method – Visualization and summary for the simplex method.7分钟

2-16: The tableau representation – An example.5分钟

2-17: The tableau representation – Another example.8分钟

2-18: Solving unbounded LPs.5分钟

2-19: Infeasible LPs – The two-phase implementation.9分钟

2-20: Infeasible LPs – An example.10分钟

2-21: Computers – Gurobi and Python for LPs.5分钟

2-22: Computers – An example.7分钟

2-23: Computers – Model-data decoupling.6分钟

2-24: Closing remarks.5分钟

1 个练习

Quiz for Week 220分钟

周

周 3

完成时间为 2 小时

The Branch-and-Bound Algorithm

Integer programming is a special case of linear programming, with some of the variables must only take integer values. In this week, we introduce the concept of linear relaxation and the Branch-and-Bound algorithm for solving integer programs.

完成时间为 2 小时

16 个视频（总计 121 分钟）

16 个视频

3-0: Opening.5分钟

3-1: Introduction.3分钟

3-2: Linear relaxation.4分钟

3-3: Properties of linear relaxation.9分钟

3-4: Idea of branch and bound.6分钟

3-5: Example 1 for branch and bound (1).6分钟

3-6: Example 1 for branch and bound (2).8分钟

3-7: Example 2 for branch and bound.5分钟

3-8: Remarks for branch and bound.8分钟

3-9: Solving the continuous knapsack problem.10分钟

3-10: Solving the knapsack problem with branch and bound.11分钟

3-11: Heuristic algorithms.10分钟

3-12: Performance evaluation.7分钟

3-13: Remarks for performance evaluation.5分钟

3-14: Computers – Gurobi and Python for IPs.11分钟

3-15: Closing remarks.6分钟

1 个练习

Quiz for Week 320分钟

周

周 4

完成时间为 2 小时

Gradient Descent and Newton’s Method

In the past two weeks, we discuss the algorithms of solving linear and integer programs, while now we focus on nonlinear programs. In this week, we first review some necessary knowledge such as gradients and Hessians. Second, we introduce gradient descent and Newton’s method to solve nonlinear programs. We also compare these two methods in the end of the lesson.

完成时间为 2 小时

13 个视频（总计 102 分钟）

13 个视频

4-0: Opening.7分钟

4-1: Introduction.7分钟

4-2: Gradient descent – Gradient and Hessians.7分钟

4-3: Gradient descent – A gradient is an increasing direction.9分钟

4-4: Gradient descent – The gradient descent algorithm.10分钟

4-5: Gradient descent – Example 1.8分钟

4-6: Gradient descent – Example 2.9分钟

4-7: Newton’s method – Newton’s method for a nonlinear equation.5分钟

4-8: Newton’s method – Newton’s method for a single-variate NLPs.6分钟

4-9: Newton’s method – An example for single-variate Newton’s method.6分钟

4-10: Newton’s method – Newton’s method for multi-variate NLPs.8分钟

4-11: Computers – Gurobi and Python for NLPs.7分钟

4-12: Closing remarks.6分钟

1 个练习

Quiz for Week 420分钟

审阅

4.8

6 条评论

5 stars
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来自OPERATIONS RESEARCH (2): OPTIMIZATION ALGORITHMS的热门评论

由 HP 提供Sep 15, 2021

The Course was done earlier, hence, there was no one to answer the forums or questions, otherwise a very good course to learn about applying Python.

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Operations Research (2): Optimization Algorithms

Operations Research (2): Optimization Algorithms