Add momentequalities and momentinequalities

[apozas]

ncpol2sdpa has the ability of adding arbitrary (linear) constraints between elements of the moment matrix. Eventually we will want to implement something similar to improve the flexibility of the program. In fact, this is an easy way of imposing only some identifications with known probabilities.

EDIT: We have since long had the support for momentequalities and momentinequalities in the solveSDP_mosekFUSION, but several things need to be done before we can consider this a complete feature of the library:

• [x] Add a simple way of the users to insert them. Following the spirit of the remaining functionalities, I'd advocate for functions InflationSDP.set_momentequalities and InflationSDP.set_momentinequalities, that performed analogous to set_values and set_bounds.
• [ ] Write tests. We already had a hiccup in #64, and we don't want to go through the same when we implement other solvers.
• [x] Add support for them in the export functions. See https://github.com/ecboghiu/inflation/commit/352e8e4dd25f1649429f426586c51055ad4e5a20, https://github.com/ecboghiu/inflation/commit/aa312ae9eebb388360d95c39ef86ad5f958ff489 and https://github.com/ecboghiu/inflation/commit/34f0cfe7a767190705d632593bef72f7aeb35fd0.

[eliewolfe]

Looks like this is long since resolved.

[apozas]

I want to keep it open, because this feature is pretty crucial (given our new discoveries in non-network scenarios) and yet there does not exist tests for it. I think we should keep the issue open until proper tests are developed. Moreover, there is no simple way for a user to add them, and the export to other formats still does not support them.

[apozas]

No, since all the tasks here are not encompassed by #69. Moreover, albeit Task 1 can be delayed for after the first release, Task 2 is crucial for correctly handling non-networks and Task 3 is important for having a consistent package (I am happy dealing with this in the next coming days), and I think that both should be addressed before the initial release.