Course Overview-Course Content
NTU MOOC course information
Prelude
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1-1: Overview.
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1-2: The row and column views for a linear system – A two-dimensional example.
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1-3: The row and column views for a linear system – A three-dimensional example.
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1-4: Using Gaussian elimination to solve Ax=b – Nonsingular.
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1-5: Using Gauss-Jordan elimination to solve A^(-1) – Singular.
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1-6: Linear dependence and independence.
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The Simplex Method-Course Content
2-0: Opening.
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2-1: Introduction.
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2-2: Standard form – Extreme points.
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2-3: Standard form – Standard form LPs.
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2-4: Standard form – Standard form LPs in matrices.
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2-5: Basic solutions – Independence among rows.
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2-6: Basic solutions – Basic solutions.
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2-7: Basic solutions – An example for listing basic solutions.
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2-8: Basic solutions – Basic feasible solutions.
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2-9: Basic solutions – Adjacent basic feasible solutions.
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2-10: The simplex method – The idea.
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2-11: The simplex method – The first move.
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2-12: The simplex method – The second move.
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2-13: The simplex method – Updating the system through elementary row operations.
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2-14: The simplex method – The last attempt with no more improvement.
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2-15: The simplex method – Visualization and summary for the simplex method.
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2-16: The tableau representation – An example.
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2-17: The tableau representation – Another example.
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2-18: Solving unbounded LPs.
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2-19: Infeasible LPs – The two-phase implementation.
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2-20: Infeasible LPs – An example.
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2-21: Computers – Gurobi and Python for LPs.
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2-22: Computers – An example.
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2-23: Computers – Model-data decoupling.
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2-24: Closing remarks.
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The Branch-and-Bound Algorithm-Course Content
3-0: Opening.
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3-1: Introduction.
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3-2: Linear relaxation.
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3-3: Properties of linear relaxation.
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3-4: Idea of branch and bound.
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3-5: Example 1 for branch and bound (1).
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3-6: Example 1 for branch and bound (2).
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3-7: Example 2 for branch and bound.
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3-8: Remarks for branch and bound.
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3-9: Solving the continuous knapsack problem.
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3-10: Solving the knapsack problem with branch and bound.
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3-11: Heuristic algorithms.
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3-12: Performance evaluation.
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3-13: Remarks for performance evaluation.
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3-14: Computers – Gurobi and Python for IPs.
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3-15: Closing remarks.
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Gradient Descent and Newton’s Method-Course Content
4-0: Opening.
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4-1: Introduction.
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4-2: Gradient descent – Gradient and Hessians.
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4-3: Gradient descent – A gradient is an increasing direction.
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4-4: Gradient descent – The gradient descent algorithm.
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4-5: Gradient descent – Example 1.
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4-6: Gradient descent – Example 2.
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4-7: Newton’s method – Newton’s method for a nonlinear equation.
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4-8: Newton’s method – Newton’s method for a single-variate NLPs.
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4-9: Newton’s method – An example for single-variate Newton’s method.
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4-10: Newton’s method – Newton’s method for multi-variate NLPs.
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4-11: Computers – Gurobi and Python for NLPs.
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4-12: Closing remarks.
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Design and Evaluation of Heuristic Algorithms-Course Content
5-0: Opening.
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5-1: Background.
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5-2: Motivation and objective.
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5-3: Three levels of modeling.
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5-4: Conceptual modeling.
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5-5: Mathematical modeling (1).
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5-6: Mathematical modeling (2).
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5-7: Results.
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5-8: A heuristic algorithm.
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5-9: Pseudocode.
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5-10: Performance evaluation.
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5-11: Closing remarks.
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Course Summary and Future Learning Directions-Course Content
6-1: Summary and discussions.
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6-2: Preview of the next course.
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A story that never ends
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