Mathematical programming (MP) is a useful tool for optimization problems that appear everywhere in modern society. This course
presents the theoretical framework and algorithms of mathematical programming for linear and nonlinear programming problems.
To learn the basic solution methods of linear and nonlinear programming problems and to apply them to simple problems.
- To understand that programming problems in the real world can be formulated as mathematical programming problems, and to formulate simple problems by yourself. (Class schedule 1, 2, 3, 4, 5, 6)
- To understand the simplex method and duality theorem, and to solve simple linear programming problems. (Class schedule 2,3)
- To understand optimization methods for nonlinear programming problems and to solve simple problems. (Class schedule 4,5,6)
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Introduction of mathematical programing, Formulation of linear programming problem. | Preparation: Read the syllabus, and search applications of mathematical programming. | 60minutes |
| Review: Find an example yourself and formulate it into a linear programming problem. | 60minutes | ||
| 2. | Concepts, principle, and example of the simplex method | Preparation: Read Ref. (1) 2.2. | 60minutes |
| Review: Explain “the simplex method” in your own words and try to find and apply examples. | 60minutes | ||
| 3. | Relaxation problem and duality theorem | Preparation: Read Ref. (1) 2.3 | 60minutes |
| Review: Explain “the duality theorem” in your own words and try to find and apply examples. | 60minutes | ||
| 4. | Nonlinear programming problem | Preparation: Read Ref. (1) 3.1 | 60minutes |
| Review: Find an example yourself and formulate it into a nonlinear programming problem. | 60minutes | ||
| 5. | Optimization problem without constraints | Preparation: Read Ref. (1) 3.2 | 60minutes |
| Review: Explain “the optimization without constraints” in your own words and try to find and apply examples. | 60minutes | ||
| 6. | Optimization problem with constraints | Preparation: Read Ref. (1) 3.3 | 60minutes |
| Review: Explain “the optimization with constraints” in your own words and try to find and apply examples. | 60minutes | ||
| 7. | Final Exam and Comments | Review the contents of the 1th to the 6th lecture. You are expected to solve concrete problems if the general formula or algorithm is presented. | 300minutes |
| Total. | - | - | 1020minutes |
| Report | Exam | Total. | |
|---|---|---|---|
| 1. | 10% | 20% | 30% |
| 2. | 10% | 20% | 30% |
| 3. | 20% | 20% | 40% |
| Total. | 40% | 60% | - |
Grading: Reports (40%) and final exam (60%). Over 60% in total is acceptable. If you understand and explain basic notions
treated in classes and you solve problems whose levels are the same as examples treated in classes, you get over 60%.
TEXTBOOK: S. Umetani, “Mathematical Optimization: From Models to Algorithms”, Kodan-sha (in Japanese)
REFERENCE BOOK: M. Kanatani, “Easy-to-understand mathematics of optimization” Kyoritsu Shuppan (in Japanese)
REFERENCE BOOK: T. Kuno, M. Shigeno, and J. Goto, “IT Text Mathematical Optimization” Ohm-sha (in Japanese)
REFERENCE BOOK: M. Kanatani, “Easy-to-understand mathematics of optimization” Kyoritsu Shuppan (in Japanese)
REFERENCE BOOK: T. Kuno, M. Shigeno, and J. Goto, “IT Text Mathematical Optimization” Ohm-sha (in Japanese)
Understanding the contents of "Data Structure and Algorithms 2" and having a basic knowledge of calculus and linear algebras.
Mathematical skills to deal with equations are also required.
- Lunch time between 2nd and 3rd periods on Monday. E-mail contact is also available to ask questions.
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
- 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
- 12.RESPONSIBLE CONSUMPTION & PRODUCTION
Last modified : Sat Mar 19 00:20:56 JST 2022