Instructor: Can Li
Email: canli@purdue.edu
Classroom: Hampton Hall of Civil Engineering, Room 2102
Time: Tuesday and Thursday, 4:30 pm - 5:45 pm
Office: Forney Hall of Chemical Engineering, Room G027A
Office Hours: Thursday, after class
This is a graduate-level introductory course to mathematical optimization. We will cover the theory and algorithms of linear programming, mixed-integer linear/nonlinear programming, conic programming, global optimization of nonconvex problems, and decomposition algorithms for mixed-integer programs. We will motivate the algorithms using modern applications in chemical engineering, transportation, energy systems, machine learning, and control.
The course lectures will be 30% proofs, 50% algorithms and computation, and 20% modeling and applications in engineering. The homework will keep a similar portion. However, we will not have proofs in the exams since this is a class targeted at engineering students.
Previous offerings of the courses can be found below.
| Date |
Topic |
Slides |
Homework |
Handouts and Links | Video |
|---|---|---|---|---|---|
| Tue Jan 13 | Introduction to Course | slides ipad | HW1 | Pyomo Tutorial | video |
| Thu Jan 15 | Linear Algebra and Calculus Review | slides ipad | video | ||
| Tue Jan 20 | Convex sets, functions | slides ipad | video | ||
| Thu Jan 22 | Unconstrained optimization | slides ipad | HW2 | video | |
| Tue Jan 27 | Linear Programming Applications | slides ipad | video | ||
| Thu Jan 29 | Polyhedron Theory | slides ipad | HW3 | video | |
| Tue Feb 3 | Simplex Algorithm | slides ipad | video | ||
| Thu Feb 5 | Linear Programming Duality | slides ipad | HW4 | video | |
| Tue Feb 10 | Conic Programming | slides ipad | Mittelmann benchmark | video | |
| Thu Feb 12 | Langrangian Dual and Optimality Conditions | slides ipad | HW5 | video | |
| Tue Feb 17 | Nonlinear Programming Algorithms | slides ipad | video | ||
| Thu Feb 19 | Modeling of Discrete and Continuous Decisions | slides ipad | HW6 | video | |
| Tue Feb 24 | Formulating Mixed-Integer Linear Programming Models | slides ipad | practice exam 1 | video | |
| Thu Feb 26 | Mixed-Integer Linear Programming Applications | slides ipad | HW7 | video | |
| Tue March 3 | Branch and Bound | slides ipad | video | ||
| Thu March 5 | Cutting Planes | slides ipad | video | ||
| Tue March 10 | Midterm Review | ||||
| Tue March 12 | Midterm Exam | ||||
| March 17,19 | Spring break | ||||
| Tue March 24 | MIP Solvers | slides ipad | video | ||
| Thu March 26 | Nonconvex Optimization Applications | slides ipad | HW8 | video | |
| Tue March 31 | Infeasibility Detection | slides ipad | video | ||
| Thu April 2 | Convex Relaxations | slides ipad | video | ||
| Tue April 7 | Branch and Reduce | slides ipad | HW9 | video | |
| Thu April 9 | Decomposition Algorithms for MINLP | slides ipad | video | ||
| Tue April 14 | Stochastic Programming and Benders Decomposition | slides ipad | HW10 | video | |
| Thu Apr 16 | Column Generation and Dantzig Wolfe Decomposition | slides ipad | video | ||
| Tue Apr 21 | Lagrangian Relaxation and Decomposition | slides ipad | HW 11 | video | |
| Thu Apr 23 | Augmented Lagrangian and ADMM | slides ipad | HW 12 | video | |
| Tue Apr 28 | Bilevel Optimization | slides ipad | practice exam 2 | video | |
| Thu April 30 | Final Review | ipad | video |
This class will not exactly follow any textbook. But we may cover some of the content in the following textbooks.
We will use the following software
Some familiarity with linear algebra, calculus, and programming in python is required.