Problems with optimizing constraints and subsets

[kai-qu]

The system seems to have problems optimizing certain constraints. Running the following command has several problems. ./Main snap sub/twosets.sub sty/venn_comp.sty

• constraint contains(y, x) does not work well in two scenarios: 1. with any objective on the labels, or 2. if the constraint on containment starts off violated.
• In principle, the exterior point method requires constraints to be violated in the initial state (that is, the "point" lies in the exterior). Setting constraintFlag = True means that the Subset constraint is initially satisfied, which defeats the purpose. Even if the flag is false, the system does not guarantee that at least one constraint is violated, as the rng seed might be set such that the constraints happen to be satisfied.
• For some reason, if the x and y coordinates of the two sets are set to varying, then they are NaNing after one step. Only those coordinates NaN out first; the radii are fine. If the x and y coordinates are set to fixed, then there aren't problems.
• A lot of things could possibly be causing this problem. Autodiff? Initial changes made to implement the computational graph? The objective function strictSubset being written incorrectly? (Seems to work though.) A problem with circle packing and unpacking?

Temporarily resolved. To fully resolve:

• If I square both sides, will strictSubset still work as a valid penalty?
• Check if state starts in the exterior now
• Why did distance work sometimes originally?
• Document the solution with avoiding divide by zero
• Why is the optimization so slow? Might have to do with starting in exterior vs. interior
• Test the full subset program
• Regression-test the existing programs that might have NaNs
• Add test suite

[kai-qu]

Resolved. Also works for tree.sub with venn.sty.

• Should deal with tangency, as due to how EP works, the state will stop as it reaches just inside the interior region.
• Use isNan in the future to catch NaNs.
• In the future, watch out for divide-by-zeros (derivatives with variable denominators) and add epsilon strategically, or avoid those kinds of functions.