線性規劃
Linear Programming
| 節 | 週一 |
|---|---|
2 09:00–09:50 | 線性規劃 MB414（光復） 3 節連堂 |
3 10:10–11:00 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
This course focuses on theorems and algorithms for solving linear programming problems. The goal is to provide fundamentals for students who interest in taking advanced classes in a broad area of mathematical programming.
Linear algebra (recommended, but not required)
無備註
The electronic textbook is available online at the NCTU library system.
The homework will be assigned in every other week. Two midterm exams (20% on each), final exam (20%), homework (25%) and in-class performance (15%)
Preliminary
1.Set theory 2.Linear algebra 3.Polyhedral theory
- 講授：
- 6
Basic theorems
1.Simplex method 2.Degeneracy 3.Duality theorems 4.Sensitivity analysis 5.Implementations of simplex methods
- 講授：
- 15
Interior-point methods
1.Convex analysis 2.Farkas’lemma 3.Central path method 4.Lagrange multipliers 5.KKT system
- 講授：
- 15
Extensions
1.Decomposition methods 2.Network flow problems 3.Integer programming
- 講授：
- 12
Solver tutorial
1.IBM CPLEX callable library 2.Modeling language
- 講授：
- 3
- 實作：
- 3
| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction 2023-09-11(一) |
| 第 2 週 | Set theory, linear algebra 2023-09-18(一) |
| 第 3 週 | Simplex methods 2023-09-25(一) |
| 第 4 週 | Degeneracy 2023-10-02(一) |
| 第 5 週 | Simplex method in matrix notation 2023-10-09(一) |
| 第 6 週 | Midterm exam I 2023-10-16(一) |
| 第 7 週 | Duality theory 2023-10-23(一) |
| 第 8 週 | Efficiency of the simplex algorithm 2023-10-30(一) |
| 第 9 週 | CPLEX / Modeling language 2023-11-06(一) |
| 第 10 週 | Sensitivity analysis 2023-11-13(一) |
| 第 11 週 | Convex analysis 2023-11-20(一) |
| 第 12 週 | Midterm exam II 2023-11-27(一) |
| 第 13 週 | Interior-point methods 2023-12-04(一) |
| 第 14 週 | KKT system 2023-12-11(一) |
| 第 15 週 | Decomposition principle 2023-12-18(一) |
| 第 16 週 | Network flow problems 2023-12-25(一) |
| 第 17 週 | Integer programming 2024-01-01(一) |
| 第 18 週 | Final Exam 2024-01-08(一) |
Linear Programming: Foundations and Extensions 4th Edition, Robert J. Vanderbei., Springer, 2014
- 地點
- MB513
- 時間
- By appointment
- 聯絡方式
- sichen@nycu.edu.tw