Operations Research (2): Optimization Algorithms

孔令傑 (Ling-Chieh Kung)

Offered By

Operations Research (2): Optimization Algorithms

National Taiwan University

About this Course

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.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

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

Approx. 12 hours to complete

English

Subtitles: English

What you will learn

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.

Skills you will gain

AlgorithmsBusiness AnalyticsMathematical Optimization

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Flexible deadlines

Reset deadlines in accordance to your schedule.

Intermediate Level

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

Approx. 12 hours to complete

English

Subtitles: English

Instructor

孔令傑 (Ling-Chieh Kung)

副教授 (Associate Professor)

資訊管理學系 (Department of Information Management)

24,611 Learners

7 Courses

Offered by

National Taiwan University

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.

Syllabus - What you will learn from this course

Week

Week 1

2 hours to complete

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.

2 hours to complete

7 videos (Total 73 min), 1 reading, 1 quiz

7 videos

Prelude2m

1-1: Overview.8m

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

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

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

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

1-6: Linear dependence and independence.9m

1 reading

NTU MOOC course information5m

1 practice exercise

Quiz for Week 120m

Week

Week 2

3 hours to complete

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.

3 hours to complete

25 videos (Total 168 min)

25 videos

2-0: Opening.4m

2-1: Introduction.3m

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

2-18: Solving unbounded LPs.5m

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

2-20: Infeasible LPs – An example.10m

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

2-22: Computers – An example.7m

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

2-24: Closing remarks.5m

1 practice exercise

Quiz for Week 220m

Week

Week 3

2 hours to complete

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.

2 hours to complete

16 videos (Total 121 min)

16 videos

3-0: Opening.5m

3-1: Introduction.3m

3-2: Linear relaxation.4m

3-3: Properties of linear relaxation.9m

3-4: Idea of branch and bound.6m

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

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

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

3-8: Remarks for branch and bound.8m

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

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

3-11: Heuristic algorithms.10m

3-12: Performance evaluation.7m

3-13: Remarks for performance evaluation.5m

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

3-15: Closing remarks.6m

1 practice exercise

Quiz for Week 320m

Week

Week 4

2 hours to complete

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.

2 hours to complete

13 videos (Total 102 min)

13 videos

4-0: Opening.7m

4-1: Introduction.7m

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

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

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

4-5: Gradient descent – Example 1.8m

4-6: Gradient descent – Example 2.9m

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

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

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

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

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

4-12: Closing remarks.6m

1 practice exercise

Quiz for Week 420m

Frequently Asked Questions

When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I purchase the Certificate?
When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes, Coursera provides financial aid to learners who cannot afford the fee. Apply for it by clicking on the Financial Aid link beneath the "Enroll" button on the left. You’ll be prompted to complete an application and will be notified if you are approved. Learn more.
Will I earn university credit for completing the Course?
This Course doesn't carry university credit, but some universities may choose to accept Course Certificates for credit. Check with your institution to learn more. Online Degrees and Mastertrack™ Certificates on Coursera provide the opportunity to earn university credit.

More questions? Visit the Learner Help Center.

Operations Research (2): Optimization Algorithms

Operations Research (2): Optimization Algorithms