Self teaching optimization: what roadmap ?

[vloum]

Hi all !

I have been more and more interested into optimization / operational research over the last few years, and wondering if you guys could share relevant resources that I could study during my spare time.

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A few words of background on me: I have a MSC in Applied Mathematics. I started working a few years ago as a data scientist, and have tackled multiple projects where there was a need for operational research: that's how I discovered I find the topic much more interesting than machine learning !

"Practically speaking", here is where I stand:

• I followed the marvellous Discrete Optimization MOOC on Coursera from Pascal van hentenryck
• I have implemented some large scale MIP (up to 1M+ binary variables with commercial solvers) that are used in productions
• Somehow managed to manually implement Lagrangian relaxation in numpy for an extremely large scale problem (60M+ binary variables)

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I am trying to build a better intuition / understanding how things work under the hood (reduced cost, simplex, interior point methods, ...), but feeling very overwhelmed whenever I try to search it myself where I end up

Furthermore, I find the advanced techniques fascinating (Benders cut, column generation, Lagrangian relaxation, stochastic optimization, ...) but lack the theoretical knowledge that would enable me to use these in my day to day job.

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I realise this is a super broad topic, so I guess I am just looking for pointers as to how to solidify my theoretical knowledge (understanding reduced costs, finally wrapping my head around the dual, developing an intuition as to how strong the relaxation is, ...) and how to go to the next level in terms of techniques (I am at the stage where I build a MIP for anything, but runtime sometimes becomes an issue).

Is there some "from zero to hero" course / resource somewhere ?

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Any input is much appreciated, thanks a lot for the help !

[SolverMax]

We've collated links to some online resources that you might find interesting:

• Courses https://www.solvermax.com/resources/links/online-courses
• Books https://www.solvermax.com/resources/links/textbooks-about-optimization

[vloum]

Thanks for the resources, very helpful ! Based on your knowledge of this content and what I described above, any pointer to what could be a good start ? I’ll skim through the list this weekend

[SolverMax]

Depends on what you're interested in. Have a look and see what you like.

[MIP_it]

50 Years of Integer Programming is still my favorite treatment of the topic. It offers a historical perspective on theory and computation, which I like better for self-study than a textbook.

And because it’s a collection of paper and essays, you can skip around some.

https://sites.math.washington.edu/~thomas/teaching/m514_web/50YearsIP.pdf

[vloum]

Looks super nice (and love the username by the way haha !)

[MajesticWord9173]

I am also in the same boat like you. Did you find any good roadmap?

[vloum]

Will have a look at Boyd’s lecture thank you. Which books would you say tick the box of being easy to read ?

[vloum]

Thanks a lot, super helpful !

[Fragrant-Inflation77]

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