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