Optimization Theory and Methods

Course information

Optimization theory and methods focus on finding the best solution from many possibilities. It involves building and analyzing models such as linear, nonlinear, and integer programming, and solving them with methods like steepest descent, Newton’s method, simplex, and interior-point algorithms. Widely applied in machine learning, engineering, finance, and supply chain management, optimization helps improve efficiency and reduce costs.

I will post lecture slides for every class. There is no required textbook. However, the course will loosely follow a text by Ravindra K. Ahuja, Network Flows: Theory, Algorithms, and Application . In addition, I will recommend some other books for those who are interested in exploring the subject further. Bertsimas, D., and J.N. Tsitsiklis. Introduction to Linear Programming. Larson, R.C., and A.R. Odoni. Urban Operations Research. Fudenberg, D., and J. Tirole. Game Theory. Again, it is not necessary to buy this text

The following schedule is tentative and subject to change.

Week	Date	Topic	Readings
1	Sep 18	Chapter 0: Course Introduction Chapter 1: Operations Research for Real-World Decision-Making Chapter 2: Modeling Linear Optimization Problem	Notes: Chapter 0 [ps] [pdf]. Chapter 1 [ps] [pdf]. Chapter 2 [ps] [pdf].
2	Sep 25	Chapter 3: Solving Linear Optimization Problems Chapter 4: Integer Optimization Problems.	Notes： Chapter 3 [ps] [pdf] Chapter 4 [ps] [pdf]
4	Oct 9	Chapter 5: Network Model	Notes： Chapter 5 [ps] [pdf]
5	Oct 16	Chapter 6: Shortest Paths and Minimum Spanning Trees	Notes：
6	Oct 23	Chapter 6: Shortest Paths and Minimum Spanning Trees Chapter 7: Tours and Routings	Notes：
7	Oct 30	Chapter 8: INTRACTABILITY Chapter 9: Introduction to Game Theory	Notes：
8	Nov 6	Chapter 10: Nash Equilibrium Chapter 11: Multi-Stage Games	Notes：
9	Nov 13	Chapter 12: Introduction to AI Algorithms	Notes：

Grading	Percentage	Instruction
Attendance/Discussio	5%	When I took the course, I tried my best to attend every discussion and ask questions whenever I was confused!
Course Project	35%	Report (15%), presentation (10%) and peer review (10%)
Final exam	60%	Students are permitted to bring a single A4 sheet into the exam room to record essential information. Electronic devices are not allowed.

be able to read mathematical notation and terminology fluently
become comfortable with mathematical thinking that allows you to write clean, logical, proofs
become familiar with a number of discrete structures that are used throughout computer science
achieve a certain clarity of thinking and expression that (as a side effect) enables you to write correct and efficient code more easily.

Attend all classes including X-hours, of which I may use all of.
Students are expected to be respectful of their peers and the instructor. This includes not talking while others are talking, not using electronic devices in class, and not engaging in any other behavior that is disruptive to the learning environment.
All exams (include Intermediate exams) submitted for credit must be your own (without help for any electronic devices).
If you feel that the grader has not graded accurately then you should compose an email/wechat clearly writing down which problem and your reason why you think the grading is incorrect. If you are unsatisfied by the grader's response, then you can email the me (kejiwei@tongji.edu.cn) for a full regrade. I will look at the entire problem set and re-grade it completely.