todo.txt

## TODO
- transform Y solution to selection of edges? 
- why and how is L approximating MSS?
- torch.optim.cuda? CuPy?
- apply timing function to check total time but also to identify areas for optimization
- check minimal eigenvalue computation theta_tilde, why?
- selection of parameters?
- Store all iterations and plot Y-vector and objective function (lagrangian)
- LANCElOT method for selecting adaptive beta?
- Check if approx optimal for the SDP, using duality gap? (also, compare to nx function (approximate))
  Plot fluctuations in nx function to highlight not an exact number. Boxplot between this and HALLaR for a few runs.
  (On a really small graph check with known MSS)
- We dont necesarrily need THE optimal solution because of relaxation, but if almost it would be good 
- Test gradient function against finite difference
- resolve global variables
- How formulate trace constraint? Quadratic instead of abs.? Compare ineq/eq constraint
- compare built in gradient with provided gradient
- np.sum(np.square( -> np.norm(, ord = "fro")))

- describe computation to avoid storing X in lagrangian (see image from meeting 23/5) C*X = (CY)*Y^T
- comment reformulation of trace constraint as frobenius norm constraint? Do we need to square the frobenius norm again for it to be smooth?
- trace(YYT) -> fr_norm(Y)**2
- Try other solvers