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（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 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.
無備註
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
1. Branch strategies 2. Node selections 3. Cutting planes 4. Learning-based methods for B&C algorithm designs
- 講授：
- 6
- 示範：
- 3
Decomposition methods
1. Branch-and-price algorithms 2. L-shaped methods 3. Progressive hedging algorithms 4. Automatic decomposition methods
- 講授：
- 6
- 示範：
- 6
- 實作：
- 6
Other topics & applications
1. Disjunctive programming 2. Numerical error issues 3. Applications in manufacturing and machine learning
- 講授：
- 6
- 示範：
- 3
- 實作：
- 6
Short Reviews and Preliminaries
1. Polyhedral theorems 2. Convex analysis 3. Complexity theorems
- 講授：
- 6
| 週次 | 主題 |
|---|---|
| 第 1 週 | Mathematical Programming basics 2024-02-19(一) |
| 第 2 週 | Mathematical Programming basics 2024-02-26(一) |
| 第 3 週 | Valid inequality theorems / Reformulations & Strong formulations 2024-03-04(一) |
| 第 4 週 | Basics and recent developments in branch-and-bound algorithms 2024-03-11(一) |
| 第 5 週 | Cutting planes methods 2024-03-18(一) |
| 第 6 週 | Decomposition principles 2024-03-25(一) |
| 第 7 週 | L-shaped methods 2024-04-01(一) |
| 第 8 週 | Branch-and-price algorithms 2024-04-08(一) |
| 第 9 週 | Lagrangian based methods / Progressive hedging algorithms 2024-04-15(一) |
| 第 10 週 | Recent developments in automatic decompositions 2024-04-22(一) |
| 第 11 週 | Disjunctive Programming 2024-04-29(一) |
| 第 12 週 | Recent developments in Disjunctive Programming 2024-05-06(一) |
| 第 13 週 | Application in manufacturing 1: Lot-sizing scheduling problems MILP models and solution approaches 2024-05-13(一) |
| 第 14 週 | Application in manufacturing 2: Job-shop scheduling problems MILP models and solution approaches 2024-05-20(一) |
| 第 15 週 | Application 3: Support vector machine MILP models and solution approaches 2024-05-27(一) |
| 第 16 週 | Application 4: Network optimization problems and solution approaches 2024-06-03(一) |
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