Course Overview-Course Content
NTU MOOC course information
Prelude
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1-1: Overview.
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1-2: Reviewing the simplex method.
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1-3: The simplex method in matrices.
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1-4: Examples.
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Duality-Course Content
2-0: Opening.
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2-1: Introduction.
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2-2: Primal-dual pairs – The first example.
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2-3: Primal-dual pairs – More examples.
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2-4: Primal-dual pairs – General rule.
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2-5: Weak duality and sufficiency of optimality.
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2-6: Dual optimal solution and strong duality.
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2-7: An example for the theorems.
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2-8: Complementary slackness.
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2-9: Motivating examples for shadow prices.
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2-10: Shadow prices.
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2-11: Shadow prices and duality.
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2-12: Computers – Gurobi and Python for shadow prices.
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2-13: Closing remarks.
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Sensitivity Analysis and Dual Simplex Method-Course Content
3-0: Opening.
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3-1: Introduction.
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3-2: New variable – Motivation.
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3-3: New variable – Solution.
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3-4: New constraint – Motivation.
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3-5: Dual simplex – Idea.
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3-6: Dual simplex – Example and remark.
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3-7: Closing remarks.
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Network Flow-Course Content
4-0: Opening.
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4-1: Introduction.
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4-2: MCNF problems.
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4-3 LP formulation for MCNF
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4-4: Total unimodularity.
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4-5: MCNF and total unimodularity.
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4-6: Transportation problems.
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4-7: Assignment and transshipment problems.
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4-8: Shortest path and maximum flow problems.
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4-9: Computers – Gurobi and Python for network flow.
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4-10: Closing remarks.
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Convex Analysis-Course Content
5-0: Opening.
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5-1: Motivating examples.
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5-2: Convex sets and functions.
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5-3: Global optimality and extreme point.
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5-4: Convex programming.
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5-5: Convexity of twice differentiable functions.
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5-6: Example – EOQ
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5-7: Second-order derivatives.
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5-8: Positive semi-definiteness.
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5-9: Analytically solving multi-variate NLPs.
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5-10: Example – Two-product pricing.
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5-11: Computers – Implementation of gradient descent.
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5-12: Closing remarks.
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Lagrangian Duality and the KKT condition-Course Content
6-0: Opening.
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6-1: Motivation.
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6-2: Lagrange relaxation.
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6-3: An example of Lagrange relaxation.
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6-4: Weak duality of Lagrange relaxation.
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6-5: The KKT condition.
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6-6: Visualizing the KKT condition.
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6-7: Example 1 of applying the KKT condition.
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6-8: Example 2 of applying the KKT condition.
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6-9: The KKT condition in general.
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6-10: More about Lagrange duality.
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6-11: Convexity and strong duality of Lagrange relaxation.
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6-12: An example of Lagrange duality.
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6-13: Lagrange duality vs. LP duality.
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6-14: Closing remarks.
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Case Study-Course Content
7-0: Opening.
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7-1: Introduction.
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7-2: Simple linear regression.
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7-3: Solving the simple linear regression problem.
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7-4: Remarks and other regression models.
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7-5: Support vector machine.
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7-6: Formulating the SVM model.
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7-7: Simplifying the objective function.
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7-8: SVM for imperfect separation.
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7-9: Dualization for the SVM problem (1).
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7-10: Dualization for the SVM problem (2).
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7-11: Convexity of the dual program.
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7-12: Final remarks.
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7-13: Closing remarks.
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Course Summary and Future Learning Directions-Course Content
8-1: Summary and discussions.
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8-2: Preview for the future.
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A story that never ends.
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