[docs] add Transitioning from MATLAB tutorial

[odow]

Cherry-picked from https://github.com/jump-dev/JuMP.jl/pull/3697

Preview: https://jump.dev/JuMP.jl/previews/PR3698/tutorials/getting_started/transitioning_from_matlab/

https://jump.dev/JuMP.jl/previews/PR3698/tutorials/transitioning/transitioning_from_matlab/

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[araujoms]

I don't have write access anymore since this PR is now in your branch.

[odow]

I don't have write access anymore since this PR is now in your branch.

Yeah. I changed it here so that we can get a preview: https://jump.dev/JuMP.jl/previews/PR3698/tutorials/getting_started/transitioning_from_matlab/

[araujoms]

Maybe it is worth it adding a paragraph explaining Symmetric and Hermitian?

[blegat]

It's also worth mentioning the difference between YALMIP and JuMP according to dualization. YALMIP is always in image form / geometric conic form while in JuMP it depends on the solver. See section 2.1 of the MOI paper for instance. You can refer to https://jump.dev/JuMP.jl/stable/tutorials/conic/dualization/

[odow]

Maybe it is worth it adding a paragraph explaining Symmetric and Hermitian?

I'd like to keep this tutorial pretty tightly scoped to focus on JuMP/YALMIP/CVX.

It is not the place for this tutorial to be a cheatsheet of every difference between Julia and MATLAB. Symmetric and Hermitian should be reasonably self-evident. If it isn't users can always look up the Julia documentation.

[odow]

It's also worth mentioning the difference between YALMIP and JuMP according to dualization.

Is this necessary for users transitioning from MATLAB? It seems in the weeds. I'd prefer we left it out and got feedback first.

[araujoms]

It is not the place for this tutorial to be a cheatsheet of every difference between Julia and MATLAB. Symmetric and Hermitian should be reasonably self-evident. If it isn't users can always look up the Julia documentation.

The difference is that with YALMIP and CVX one needs to do a = 0.5*(a+a') over and over again, to make sure your matrices are exactly Hermitian, whereas with JuMP this doesn't matter, you just have to wrap them in Hermitian.

[blegat]

Is this necessary for users transitioning from MATLAB? It seems in the weeds. I'd prefer we left it out and got feedback first.

This is the n°1 comment people have when coming from YALMIP (see for instance https://discourse.julialang.org/t/yalmip-vs-jump/30776/10 and https://discourse.julialang.org/t/jump-sumofsquares-generate-sdps-with-18x-more-constraints-than-yalmip/65377/15). It can just be a small note refering to the relevant part of the doc. (sorry I closed, missed click)

[araujoms]

I also think it would be worth it such a remark, it has a large impact on performance.

[odow]

Merging because this is good enough for now. If needed, we can make tweaks in smaller PRs, instead of hashing everything out here. (There are already 56 comments!)