Welcome to Global_Optimization_NTNU Discussions!

[avinashresearch1]

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:

1. 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.

2. 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.

[avinashresearch1]

Colloquiums:

The plan is to give the 5 two hour colloquiums/discussions as below. The idea for the format is as below: First, participants are expected to familiarize themselves with some material prior to the colloquium. Mostly, this will involve watching lectures Prof. Barton recorded in 2021 which have been uploaded to blackboard. This "preparation" work is listed

1. Week 39. - Formulation Optimization Problems with JuMP in Julia. JuMP is an open-source alternative to GAMS that is substantially easier/more convenient to use in my opinion.

• Preparation work: Please have Julia and JuMP installed. Instructions are here: https://jump.dev/JuMP.jl/stable/installation/
• We will go through some tutorials listed here during the colloquium depending on student interest.
  https://jump.dev/JuMP.jl/stable/tutorials/getting_started/introduction/

2. Week 41. - Mixed-Integer Linear Programming.

• Preparation - Please watch the recorded lectures 15-19 from blackboard.
• I will present a 30 minute summary of the lectures and we will discuss a couple of homework problems.

3. Week 43 - Benders decomposition

• Preparation - Please watch lecture 27, and 28/29 on blackboard.
• I will present a 30 minute summary of the lectures and we will discuss a couple of homework problems.

4. Week 45 - Extensions to Benders decomposition

• Continuation from previous.

5. Week 47 - TBD

[avinashresearch1]

Further instructions if necessary for installing Julia in Windows for VSCode
In general, follow: https://code.visualstudio.com/docs/languages/julia.

• Please make sure to install Julia using administrator.
• Remember to add Julia to path.
• To configure the Julia extension: https://marketplace.visualstudio.com/items?itemName=julialang.language-julia

If you would like to configure settings within VScode, please checkout: >File>Preferences>Settings>Extensions>Julia.
It may be easiest to Edit the settings.json file to cross-check that the "julia.environmentPath" key is set to the path in the binary.

Say you open a desired folder, you can create a Julia file of any names with the .jl filename.

If you type in some Julia code inside this .jl file and run it or type: Ctrl + Enter, you should be have the Julia repl launched in the terminal.

• Optional but recommended is to work with separate environments for all packages, created using Project.toml files or Julia_package.

• You may launch, Julia's PkgManager using the ] key from the Repl. This allows you to add packages from the general Julia registry, e.g., ]add JuMP

[avinashresearch1]

Solver list: https://jump.dev/JuMP.jl/stable/installation/