Learn about several important mathematical programming problems and their solutions, including linear mathematical programming,
combinatorial optimization, network planning, and nonlinear mathematical programming.
Learn about several important mathematical programming problems and their solutions, including linear mathematical programming,
combinatorial optimization, network planning, and nonlinear mathematical programming.
- understand the basic idea of linear mathematical programming and simplex method.
- understand the formulation of combinatorial optimization and its simple algorithms
- understand several typical algorithms of nonlinear mathematical programming
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Guidance, mathematical programming models | Prepare mathematical programming models | 190minutes |
| 2. | Linear mathematical programming 1 (basic solution and optimal solution) | Review of Linear mathematical programming problems learned at System Engineering B | 190minutes |
| 3. | Linear mathematical programming 2 (simplex method 1) | Summarize the algorithm of simplex method with exercises | 190minutes |
| 4. | Linear mathematical programming 3 (simplex method 2, introduction of dual problem) | Review the duality property and check how to use it. | 190minutes |
| 5. | Linear mathematical programming 4 (dual problem and dual theorem) | Review of the algorithms learned by now. | 190minutes |
| 6. | Report 1 and Review | Review linear programming and prepare for report 1 | 190minutes |
| 7. | Introduction of combinatorial optimization | Review the related part in the textbook, including basic definitions in graph theory. | 190minutes |
| 8. | Solve combinatorial optimization by branch and bound method | Try to understand why branch and bound method works | 190minutes |
| 9. | Review of Report 1 and Explain Report 2 | Review of Report 1 and what you have learned by now | 190minutes |
| 10. | Nonlinear mathematical programming 1 (gradient and Hessian matrix of a function) | Review of basic calculus in optimization problems | 190minutes |
| 11. | Nonlinear mathematical programming 2 (optimization without constraints) | Review basic knowledge about positive/negative definite matrices. Summarize the algorithms with exercises | 190minutes |
| 12. | Review of Report 2 and nonlinear programming 3 (steepest descent method) | Review of Report 2 and try to solve simple NP problems with steepest descent method | 190minutes |
| 13. | Nonlinear mathematical programming 3 (Newton method) | Try to solve simple NP problems with Newton method method | 190minutes |
| 14. | Report 3 and Review of the whole course | Review of the whole course | 190minutes |
| Total. | - | - | 2660minutes |
| Report 1,2,3 | Total. | |
|---|---|---|
| 1. | 30% | 30% |
| 2. | 30% | 30% |
| 3. | 40% | 40% |
| Total. | 100% | - |
Evaluation by three reports
Report 1: 30%
Report 2: 30%
Report 3: 40%
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Pass when reaching 60% of the whole evaluation, or in other words, reaching the level of using Simplex Method, Branch and Bound Method, and Newton Method to solve simple numerical problems.
Report 1: 30%
Report 2: 30%
Report 3: 40%
--------
Pass when reaching 60% of the whole evaluation, or in other words, reaching the level of using Simplex Method, Branch and Bound Method, and Newton Method to solve simple numerical problems.
Fukushima, M.: Introduction to Mathematical Programmning (New Version), Asakura Publishing
- Course that cultivates a basic self-management skills
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
Last modified : Sun Mar 21 15:23:18 JST 2021