About this Course

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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.

Flexible deadlines

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Shareable Certificate

Earn a Certificate upon completion

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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

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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

Algorithms
Business Analytics
Mathematical Optimization

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own 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

Could your company benefit from training employees on in-demand skills?

Try Coursera for Business

Instructor

Instructor rating

4.8/5 (21 Ratings)

孔令傑 (Ling-Chieh Kung)

副教授 (Associate Professor)

資訊管理學系 (Department of Information Management)

65,632 Learners

8 Courses

Syllabus - What you will learn from this course

Week

1

Week 1

2 hours to complete

Course Overview

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 information1m

1 practice exercise

Quiz for Week 120m

Week

2

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

3

Week 3

2 hours to complete

The Branch-and-Bound Algorithm

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

4

Week 4

2 hours to complete

Gradient Descent and Newton’s Method

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

Reviews

4.8

11 reviews

5 stars
87.30%
4 stars
9.52%
2 stars
1.58%
1 star
1.58%

TOP REVIEWS FROM OPERATIONS RESEARCH (2): OPTIMIZATION ALGORITHMS

by HPSep 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.

View all reviews

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Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

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Operations Research (2): Optimization Algorithms