Update AC/DC docs

[klamike]

This branch continues from mt/ac-docs:

• Switch to MathJax3 (MathJax is deprecated)
• Utility functions for reusing our definitions.tex file
• Slightly widened the docs-main div so the labels fit
• Updated AC docs
• Updated DC docs

Note this version doesn't have the corresponding dual next to each constraint / in the data table.

https://ai4opt.github.io/OPFGenerator/previews/PR153/opf/acp/

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

see 1 file with indirect coverage changes

[mtanneau]

@klamike should I close #151 or merge this branch into mine? If the latter, can you update the target branch for the PR please?

[klamike]

@mtanneau If you like this one, close #151

[mtanneau]

Note this version doesn't have the corresponding dual next to each constraint / in the data table.

The reason for indicating the dual variables in bracket is because I want to (eventually) write down the dual formulations as well.
I can do that in a separate PR, and it doesn't require indicating dual variables in the primal formulation... but it will (re)introduce the mathematical symbols for dual variables.

[klamike]

Makes sense. Note our dual definitions are already in the definitions.tex so it shouldn't take long to add them.

[mtanneau]

Overall comment on the model: we've encountered some issues with the sign of dual variables for constraints that are written like

@constraint(model, x + y == z)

where x, y, z are all JuMP.VariableRefs. Namely, JuMP may end up with x + y - z == 0 or z - x - y == 0 (I assume there is some consistency in how that transformation is done, but I don't know what it is). We ended up with dual variables that were negated compared to what we expected :(

I wrote down all the constraints with variables on the left and constant terms on the right to avoid that risk.
Again, no impact on the primal, but it can change the sign of dual variables, so I'd like to have as clear conventions as possible.

[mtanneau]

Small notation change on entering/exiting arcs 🙏

[mtanneau]

There remains one thing that I feel strongly about: writing the constraints with only constant terms in the RHS.
I feel strongly about it because it's been an issue for us in the past when working on dual formulations.

I can make the change in the same PR as when I add the dual formulations.

[mtanneau]

@mtanneau is in charge of adding the dual stuff in a later PR