Operations Research (3): Theory 

Prelude

1-1: Overview.

1-2: Reviewing the simplex method.

1-3: The simplex method in metrics.

1-4: Examples.

NTU MOOC course information

Quiz for Week 1

2-0: Opening.

2-1: Introduction.

2-2: Primal-dual pairs ? The first example.

2-3: Primal-dual pairs ? More examples.

2-4: Primal-dual pairs ? General rule.

2-5: Weak duality and sufficiency of optimality.

2-6: Dual optimal solution and strong duality.

2-7: An example for the theorems.

2-8: Complementary slackness.

2-9: Motivating examples for shadow prices.

2-10: Shadow prices.

2-11: Shadow prices and duality.

2-12: Computers ? Gurobi and Python for shadow prices.

2-13: Closing remarks.

Quiz for Week 2

3-0: Opening.

3-1: Introduction.

3-2: New variable ? Motivation.

3-3: New variable ? Solution.

3-4: New constraint ? Motivation.

3-5: Dual simplex ? Idea.

3-6: Dual simplex ? Example and remark.

3-7: Closing remarks.

Quiz for Week 3

4-0: Opening.

4-1: Introduction.

4-2: MCNF problems.

4-3: Total unimodularity.

4-4: MCNF and total unimodularity.

4-5: Transportation problems.

4-6: Assignment and transshipment problems.

4-7: Shortest path and maximum flow problems.

4-8: Computers ? Gurobi and Python for network flow.

4-9: Closing remarks.

Quiz for Week 4

5-0: Opening.

5-1: Motivating examples.

5-2: Convex sets and functions.

5-3: Global optimality and extreme point.

5-4: Convex programming.

5-5: Convexity of twice differentiable functions.

5-6: Example ? EOQ

5-7: Second-order derivatives.

5-8: Positive semi-definiteness.

5-9: Analytically solving multi-variate NLPs.

5-10: Example ? Two-product pricing.

5-11: Computers ? Implementation of gradient descent.

5-12: Closing remarks.

Quiz for Week 5

6-0: Opening.

6-1: Motivation.

6-2: Lagrange relaxation.

6-3: An example of Lagrange relaxation.

6-4: Weak duality of Lagrange relaxation.

6-5: The KKT condition.

6-6: Visualizing the KKT condition.

6-7: Example 1 of applying the KKT condition.

6-8: Example 2 of applying the KKT condition.

6-9: The KKT condition in general.

6-10: More about Lagrange duality.

6-11: Convexity and strong duality of Lagrange relaxation.

6-12: An example of Lagrange duality.

6-13: Lagrange duality vs. LP duality.

6-14: Closing remarks.

Quiz for Week 6

7-0: Opening.

7-1: Introduction.

7-2: Simple linear regression.

7-3: Solving the simple linear regression problem.

7-4: Remarks and other regression models.

7-5: Support vector machine.

7-6: Formulating the SVM model.

7-7: Simplifying the objective function.

7-8: SVM for imperfect separation.

7-9: Dualization for the SVM problem (1).

7-10: Dualization for the SVM problem (2).

7-11: Convexity of the dual program.

7-12: Final remarks.

7-13: Closing remarks.

Quiz for Week 7

8-1: Summary and discussions.

8-2: Preview for the future.

A story that never ends.

Quiz for Week 8