Here is the material for the course "Tópicos em Otimização" (Topics in Optimization) lectured by me, João Dionísio, at Faculdade de Ciências da Universidade do Porto, spanning March and April 2023. As it stands, the written documents are incomplete (but the slides contain more information), and several exercise and examples are missing. In the lecture notes, this is my estimation for what is missing.
- Convex Optimization: 80%. Mainly exercises are missing, I don't plan it to be a big chapter.
- Linear Programming: 80%. Need to add more intuition on the dual and a section on reduced cost. Most exercises are missing the solution.
- Complexity theory: 70%. Being a suplementary chapter, it's missing exercises. It may have to be restructured, and I need to talk more about NPc problems.
- Integer Programming: 55%. It lacks many images, heuristics that are in the slides, and more detail on the implementation. B&B section needs to be improved.
- Decomposition Methods: 60%. Slides have more information, the algorithms need more detail. Exercises are missing.
Some proofs are also missing, and some results that weren't used need to be removed. I also need to do many rereads of the document.
Besides the theory, I also want to greatly expand the weight of PySCIPOpt on the document. Using it on the example and the solved exercises, and also to implement some algorithms. The goal will be to provide an introduction to optimization mixed with a tutorial for PySCIPOpt.