進階數學規劃
Advanced Topics in Mathematical Programming
| 節 | 週一 |
|---|---|
2 09:00–09:50 | 進階數學規劃 MB414 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 class is mainly designed for graduate students interested in fundamental theorems and recent advances in Linear Programming, Mixed-integer Linear Programming (MILP), and Stochastic Programming. Students are required to review research papers in the above areas and discuss their recent developments with the class. Also, we will design computational assignments for students to implement state-of-the-art algorithms for solving optimization problems in scheduling, network optimization, and other fields of modern applications.
1. Students must have taken Linear Programming (MGEM30052). 2. Equipped with solid knowledge in linear programming and integer programming. 3. Familiar with CPLEX or Gurobi callable libraries.
This is an English lecture class.
Each student will present research papers on a designated topic. Students' scores will be evaluated based on the quality of their presentations, submitted documents, and in-class performances.
- Branch-and-cut algorithms
- Decomposition methods
- Other topics & applications
- Short Reviews and Preliminaries
| 週次 | 主題 |
|---|---|
| 第 1 週 | Mathematical Programming basics |
| 第 2 週 | Mathematical Programming basics |
| 第 3 週 | Valid inequality theorems / Reformulations & Strong formulations |
| 第 4 週 | Basics and recent developments in branch-and-bound algorithms |
| 第 5 週 | Cutting planes methods |
| 第 6 週 | Decomposition principles |
| 第 7 週 | L-shaped methods |
| 第 8 週 | Branch-and-price algorithms |
| 第 9 週 | Lagrangian based methods / Progressive hedging algorithms |
| 第 10 週 | Recent developments in automatic decompositions |
| 第 11 週 | Disjunctive Programming |
| 第 12 週 | Recent developments in Disjunctive Programming |
| 第 13 週 | Application in manufacturing 1: Lot-sizing scheduling problems MILP models and solution approaches |
| 第 14 週 | Application in manufacturing 2: Job-shop scheduling problems MILP models and solution approaches |
| 第 15 週 | Application 3: Support vector machine MILP models and solution approaches |
| 第 16 週 | Application 4: Network optimization problems and solution approaches |
We do not request students to prepare textbooks. However, most fundamentals introduced in this class are from the following references: -Integer and Combinatorial Optimization, by George Nemhauser and Laurence Wolsey -Introduction to Stochastic Programming, Second Edition, by John R. Birge and Francois Louveaux
- 地點
- T.B.D.
- 時間
- By appointment
- 聯絡方式
- sichen@nycu.edu.tw