Implementing LOA and its infinite version.

[dnguyen227]

Implements LOA with two main components.

• a primary NLP — the model reformulated by an inner_method (BigM, MBM, or Hull) with the disjunct binaries fixed at the current selection, and
• a master MILP that accumulates outer-approximation and no-good cuts until its bound meets the incumbent.

For the infinite implementation, the flow is as follows.
Starting from Infinite GDP,

1. Reformulate with the inner method (still infinite).
2. Transcribe once for the primary NLP.
3. Copy its variables + linear constraints this is the master (MILP) (I stay in this form for adding cuts and resolving).
4. Fix a combo on the transcribed NLP -> Solve.
5. Emit cuts into the transcribed master.

[codecov]

Codecov Report

❌ Patch coverage is 97.39292% with 14 lines in your changes missing coverage. Please review.
✅ Project coverage is 99.07%. Comparing base (48a1ac5) to head (049f4e7).

Files with missing lines	Patch %	Lines
src/loa.jl	96.54%	12 Missing ⚠️
src/utilities.jl	98.03%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #137      +/-   ##
==========================================
- Coverage   99.51%   99.07%   -0.45%     
==========================================
  Files          17       18       +1     
  Lines        2061     2582     +521     
==========================================
+ Hits         2051     2558     +507     
- Misses         10       24      +14     

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[dnguyen227]

@pulsipher good for review.

[pulsipher]

This took a lot of work. My main concern is that LOA is not really a reformulation method and we are trying to force it through the reformulation API, which has some gotchas. I suspect we will need a different workflow like how Pyomo.gdp does for methods like LOA.

[pulsipher]

This seems like something to avoid, is it not possible to only store it in `_Hull'?

[pulsipher]

The problem I see with this workflow is that instead of reformulating, this actually just solves the problem as a solver. What happens if the user then calls optimize! afterward?