📘 Large-Scale Integer Programming
A USTC course on optimization and reinforcement learning methods
📍 Summer 2025 · USTC East Campus Room 5205
👨🏫 Instructor: Prof. Lan Lu, Prof. Zhi Wang
🧑💻 Teaching Assistant: Long Chen (lchen1307@mail.ustc.edu.cn)
🔗 Quick Navigation
Overview · Slides · Quizzes · Assignments
🧭 Course Overview
This course introduces essential algorithmic techniques for solving large-scale problems in integer programming and reinforcement learning, taught by Prof. Lan Lu and Prof. Zhi Wang, respectively.
It covers modeling, LP relaxation, duality, and exact algorithms such as branch-and-bound and cutting planes, along with decomposition methods like column generation and Benders decomposition.
On the learning side, the course explores both classical reinforcement learning—such as dynamic programming and temporal-difference methods—and modern approaches including deep RL and recent developments involving large language models (LLMs).
Through a combination of theory and implementation, students will learn to build, analyze, and apply advanced optimization and learning models to real-world problems. Grades will be based on attendance, in-class quizzes, and homework assignments.
📚 Course Topics and Slides
| Course | Catagory | Topic | Slides |
|---|---|---|---|
| 1 | IP | Foundations of IP: Modeling and Formulation | Download |
| 2 | IP | Formulation Strategies and Logical Constraints | Download |
| 3 | IP | Compactness, Reformulation, and Geometry in IP | Download |
| 4 | IP | Computational MILP: Branch and Bound | Download |
| 5 | IP | Duality and Value Functions in MILP | Download |
| 6 | IP | Relaxations and Lagrangian Duality | Download |
| 7 | IP | Branch-and-Bound Search Strategies | Download |
| 8 | IP | Separation, Optimization, and Cutting-Plane | Download |
| 9 | IP | Cutting Plane Generation | Download |
| 10 | IP | Column Generation and Applications | Download |
| 11 | IP | Constraint Decomposition in Integer Programming | Download |
| 12 | IP | Variable Decomposition and Benders’ Decomposition | Download |
| 13 | IP | Heuristics and Neighborhood Search | Download |
| 14 | RL | Dynamic Programming | Download |
| 15 | RL | Monte Carlo and Temporal-Difference Learning | Download |
| 16 | RL | Introduction to Deep Reinforcement Learning | Download |
| 17 | RL | Policy Gradients | Download |
| 18 | RL | Advanced Policy Gradients | Download |
| 19 | RL | Actor-Critic Algorithms | Download |
| 20 | RL | Value Function Methods | Download |
| 21 | RL | Deep Q-Learning | Download |
New slides and readings will be available by 7 PM each day.
📝 In-class Quizzes
Short quizzes will be conducted during lectures to reinforce key concepts and assess understanding.
| Date | Quiz Topic | Format | Solution | |
|---|---|---|---|---|
| July 10 | Strong Formulation | Proof | Download | None |
| July 11-1 | Parameter Optimization | Calculation | Download | None |
| July 11-2 | Lagrangian Relaxation | Proof | Download | None |
📥 Assignments
There will be a few assignments:
| HW | Topic | Due |
|---|---|---|
| None | None | None |
Assignments should be submitted as PDF or ZIP via the submission form before the deadline.
📌 For updates, resources, and slides, please check the top navigation bar regularly.