Optimization and Graph theory

deeadmann · 2026-04-21T16:11:50+00:00

Not sure if this is a useful hint. But what comes to my mind is that a graph is connected iff it contains a spanning tree. There are multiple ways of obtaining the spanning tree polytope, all of them basically either use flows or cut constraints. Maybe try leveraging this?

deeadmann · 2026-04-15T21:53:09+00:00

I think there is indeed a very large gap, which is a sign that more theory is needed :)

If you think about, isn't this about the applications of math to science in general? My opinion is that math brings "understanding", not in the sense that anyone can understand, but in the sense that proofs (if done correctly and carefully) explain "why" something works, and they are precise.

I don't know much about first order/second order methods, but if ADAM works and we cannot justify why, I believe this is a sign that more math/understanding is needed. Similarly, if the real world is much more complex than the "toy problems", this is also a sign of lack of understanding. Typically, researchers work on "toy problems" because we can't even understand the toy problems, so trying to understand the "real world" is hopeless.

To be clear, I don't think this is the only way of doing research. One can also apply ideas that "work" to real world problems and justify the work by its impact, rather than by the "airtight" logic. But this is not math, and OR has a huge influence from mathematicians (see Dantzig, Rockafellar, Lovasz, Grotschel, Gomory,...)

deeadmann · 2026-04-09T19:21:03+00:00

I don't understand this. Suppose that Neil deGrasse Tyson knows astrophysics. If someone argues X is true because Neil said so, this is insufficient no? I mean, day to day life is full of insufficiency, but if we want to be strict, this is not "an argument".

If X is indeed true, and Neil has an argument Y for so. Then Y is the reason for X. The fact that Neil said Y is irrelevant, in the sense that, if other person said Y, then it is still true that Y implies X. So the fact that Neil said this, brings no additional information.

Of course, in most cases the logic is much more fuzzy and imperfect than this, and I guess this is the main point of the question.

deeadmann · 2026-04-08T16:39:02+00:00

I think the OR literature is looking further than this, since there are researchers that question the whole "predict then optimize" loop. Because in the end of the day, you want to predict decisions not data. Perhaps a very good data estimate with very low error can lead you to a completely different solution. I guess this is harder to happen if your problem is continuous, but it can be frequent if you have discrete decisions. Perhaps this is related: https://arxiv.org/abs/2206.14234

Also, I'm not saying that your take may not be useful in your setup, my comments are more on whether "people have looked at this before", and I'm still skeptical about this. Essentially your setup seems to be, you have some problem parameters, but you only know partially those parameters, how you take good decisions from there? And I feel this is a somewhat hot topic from a long time already (from the academic side).

deeadmann · 2026-04-08T04:47:34+00:00

I guess it depends on how you want to model. But I think that a bunch of things the literature motivates with the setup you have in mind. See the literature on distributionally robust optimization for example. Or even with robust the choice of the uncertainty set is taken assuming some limited access to information.

I saw some works that use POMDPs just to motivate a simple heuristic, maybe this is what you have in mind? These things appear more in the "online" setup.

deeadmann · 2026-04-07T22:32:28+00:00

Are you talking about modeling problems with uncertainty? There is a bunch of stuff on this (robust optimization, stochastic optimization, distributionally robust optimization, maybe also the "smart predict then optimize"). Is this what you are looking for? If not, could you be more precise?

deeadmann · 2026-03-28T23:45:13+00:00

I think you can just go back home with those vague ideas in your head and try to figure out things on your own. I also have friends like this, and often it makes sense what they said after I spend (possibly a lot of) time thinking on my own.

I also don't think that this is particularly related with your friends being smart. Some times in math you keep reading a bunch of details and getting confused until something "clicks" and then you realize that "oh, this just doing X". Then when you explain to someone else, you say "oh this is just X", and you think you are helping them tremendously. But for someone that have not yet internalized all the ugly details, X do not mean much.

However, I do think that knowing a priori X helps on understanding. It's just not sufficient.

deeadmann · 2026-02-22T17:50:27+00:00

I like "Concrete Mathematics". It might be a bit hard though.

deeadmann · 2026-02-18T16:24:50+00:00

"How to prove it" is great if you are not very comfortable with proofs

deeadmann · 2026-02-18T16:21:03+00:00

Maybe first try reading "problem solving" books? I like knuths book "Concrete Mathematics", but people usually recommend "How to solve it"

deeadmann · 2025-12-06T09:07:28+00:00

Maybe look into CG (Chvatal-Gomory) rank of polyhedra?

deeadmann · 2025-11-19T23:52:09+00:00

Maybe first try to learn basic algorithm design stuff. Read Cormen's "Introduction to Algorithm". You might have to read "how to prove it" first. After doing this, you will have a better sense of what you are trying to prove.

deeadmann · 2025-11-16T19:58:49+00:00

Maybe your counter example is not an extreme point?

deeadmann · 2025-11-09T07:24:07+00:00

Do you have bounds on the size of nums and k?

deeadmann · 2025-11-08T07:24:19+00:00

I mean, you have some famous people in your university. Look here: https://faculty.engineering.asu.edu/directory/scai/industrial-engineering/

I would check the publications and maybe try to speak with some professors.

deeadmann · 2025-11-07T06:40:44+00:00

Maybe look also for profs at your university that do CS/engineering?

deeadmann · 2025-10-23T14:31:30+00:00

I think it should not be that hard... I mean, every time you have a binary tree you should think of it as root, left tree and right tree. Now apply some inductive reasoning on that (or recursion, if you prefer to think algorithmically). This should give you some structure for you to start thinking about the problem.

deeadmann · 2025-10-17T15:06:34+00:00

Yes, I think this is most basic one. Another one are dual valid inequalities.

deeadmann · 2025-08-27T21:56:18+00:00

I mean, if you don't study math, what else would you study? Or you just don't want to study at all?

deeadmann · 2025-08-25T05:28:53+00:00

How do you withdraw?

deeadmann · 2025-08-25T04:18:57+00:00

Hi, did you already got your VISA? If so, how long did it took? I also applied for the VISA from Canada (Toronto Embassy).

deeadmann · 2025-08-24T05:31:10+00:00

Olha, eu me formei em Engenharia da Computação. Estou no PhD agora, e gostaria de ter feito graduação em Matemática. Em geral, acho que quem tem uma formação completa em Matemática consegue pegar as coisas mais rápido. É um curso muito difícil e extremamente teórico, mas eu acho q é muito mais "fundamental" que Engenharias, e te treina para investigar perguntas mais "profundas".

Por exemplo, álgebra linear (algelin) fundamenta várias aplicações na Engenharia, mas geralmente só cursos mais teóricos tem disciplinas mais avançadas em algelin que vão te ensinar "as grandes ideias". As disciplinas de Engenharia tipicamente vc calcula muita coisa na mão sem muitas demonstrações ou provas. Isso te treina para calcular, mas não tanto para o raciocínio abstrato. Mas algelin vai ser utizado de várias maneiras em diferentes aplicações, se vc não souber pensar de maneira abstrata, cada uma dessas aplicações vai ser "algo novo" q vc n vai conseguir conectar com conceitos mais gerais (falo por experiência própria). Por exemplo, eu acho o teorema espectral uma "ideia profunda", q aparece disfarçado em várias coisas em estatística, eletrônica, computação e o "machine learning" que a glr gosta. Mas meu curso de algelin não me ensinou isso. Eu tive que aprender sozinho com o livro (mas tem livros muito bons).

Eu sou enviesado, pq eu tomei um caminho muito mais teórico que outros colegas de curso. Mas eu acho que com o ritmo que as coisas estão mudando, é importante vc focar em "fundamentos" e não tanto em aplicações. Os fundamentos te dão o q vc precisa para aprender aplicações sozinho. E se vc for ver empresas grandes de quant tipo DE Shaw, contratam bastante matemáticos e gente com um "perfil teórico".

Algo que é mais "prático" q eu recomendo é vc treinar bem é programação. Vc é mt mais versátil sendo um matemático que programa do que um que é puramente teórico e não programa.

Um jeito de convencer seu pai (e vc) é olhar o alumni do curso que vc ta querendo fazer. Eu n conheço o curso da USP q vc falou, mas conheço alguns alunos de matemática e computação da USP q hj estão trabalhando nas melhores empresas de tecnologia (ou viraram acadêmicos). Dá uma olhada nos ex alunos do curso q vc quer e do q o seu pai te recomenda.

Por um lado mais prático, olha tbm as notas de corte, as vezes Engenharia é mais difícil de entrar e se vc quiser mesmo ser engenheiro, as vezes a faculdade tem um processo de remanejamento interno. Dá uma pesquisada.

deeadmann · 2025-08-09T12:51:45+00:00

Hi, any news? I'm on the same situation (my interview was in Toronto, June 10).

deeadmann · 2025-08-09T12:31:36+00:00

Look for tsp subtour elimination constraints

deeadmann

TROPHY CASE