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 mathematical programming.
Prerequisites are optional, but it is helpful if you have already taken the undergraduate-level Operations Research course and are familiar with the Microsoft C# or Python programming language.
無備註
The electronic textbook is available online at the elibrary 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. Environment 2. Solver APIs 3. Modeling language
- 講授：
- 3
- 實作：
- 3
| 週次 | 主題 |
|---|---|
| 第 1 週 | Linear algebra, set theory, and polyhedral theory 2025-09-01(一) |
| 第 2 週 | Simplex methods 2025-09-08(一) |
| 第 3 週 | Infeasibility, degeneracy, and unboundness 2025-09-15(一) |
| 第 4 週 | Simplex method in matrix notation 2025-09-22(一) |
| 第 5 週 | Midterm exam I 2025-09-29(一) |
| 第 6 週 | Duality theory 2025-10-06(一) |
| 第 7 週 | Efficiency and implementation details of simplex methods 2025-10-13(一) |
| 第 8 週 | Sensitivity analysis 2025-10-20(一) |
| 第 9 週 | Convex analysis 2025-10-27(一) |
| 第 10 週 | Midterm exam II 2025-11-03(一) |
| 第 11 週 | Interior-point methods 2025-11-10(一) |
| 第 12 週 | KKT system 2025-11-17(一) |
| 第 13 週 | Linear programming applications & modeling language 2025-11-24(一) |
| 第 14 週 | Stochastic programming & decomposition methods 2025-12-01(一) |
| 第 15 週 | Integer programming 2025-12-08(一) |
| 第 16 週 | Final 2025-12-15(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