Welcome to EP8199 - Global Optimization of Mixed-Integer and Non-Convex Problems Course homepage
Since many students may not have reliable access to blackboard before registration or may want to audit, this could help answer some FAQs about the course:
- Course logistics: The course has 3 main interactive components:
A 3 day live seminar held by Prof. Paul Barton from MIT on 8, 9 and 12 September, 09:15-16:00 (with lunch and coffee breaks). This will be arranged in C-201 (Kolbjørn Hejes vei 1.A, 2nd floor) for 8 and 9 September, and then probably F404 for 12 September. These will represent approximately 15 hours of lecture. The intention is to cover the following topics: Introduction and motivation for Global Optimization, Local vs Global Information, Optimality Criteria (e.g., KKT conditions), Duality theory (including with presence of nonconvexities), Interval Analysis, Convex Relaxations, Introduction to branch-and-bound for nonconvex programming
A complete set of recorded video lectures from Prof. Barton's 10.557 Mixed-Integer and Nonconvex Optimization course at MIT in 2021.
5 live two hour colloquiums held by Avinash Subramanian. The exact dates are TBD. The tentative list of topics are: i) Formulation Optimization Problems with JuMP in Julia ii) Mixed-Integer Linear Programming (MILP). Branch-and-Bound algorithm for MILPs iii) Benders decomposition for MILPs. iv) Generalized Benders Decomposition, Nonconvex Generalized Benders Decomposition v) One of: Outer Approximation, Mixed-Integer Nonconvex Programming.
The idea is for students to watch the relevant lectures prior to the colloquiums. Colloquiums will be interactive and would look at some homework problems and are not lectures.
- Exam, Grading, etc
The idea is for students to use some of the material covered in their research and write a report. Grading is pass/fail based on the report. 3. Can I do it online?
Yes, but not recommended. The recorded lectures from 2021 are fairly comprehensive so you may watch them and submit a report. It is unlikely that Prof. Barton's 3 day seminar will be streamed (since he mostly used a whiteboard to teach). However, we hope to record them if equipment is available from NTNU. The colloquiums may be streamed but would also make substantial use of a whiteboard thus physical presence is recommended. 4. What background is required?
The course lectures generally assume some mathematical maturity but try to explain a lot of concepts from basics. An attempt is also made to provide geometric intuition for the techniques. Having knowledge of calculus, some linear algebra should be sufficient. The course notes have several homework problems which mostly involve developing mathematical proofs (which would benefit from previous exposure to real analysis). However, these are optional and proof-based problems won't be discussed in the colloquia. Instead, we intend to solve certain specific example problems (where basic Matlab/Python/Julia) knowledge is sufficient. The only strict requirement is to work on a related project.
See the Discussion