sherali-adams 0.2

run k rounds of SA hierarchy

sherali_adams

A small library of functions with few dependencies to run k rounds of Sherali-Adams relaxation on a system of the form Ax <= b represented by raw numpy matrix A and array b.

notes

The constraints 0 <= y <= 1 will be added for all variables in the system returned. Send me a note if you'd like for this to be optional.

install

pip install sherali_adams

Testing

> nosetests

Ran 5 tests in 0.423s

OK

Examples

1. Run 1 round of SA on a system with 2 variables.
   A = np.matrix([1,1],[1,1]) b = np.matrix([1,1]) (AA,bb) = run_SA(1,2,A,b)
2. Find the original monomial corresponding to new variables. Here we find it for y_3 in the result above after 1 round of SA on a system with 2 variables.(0 based indexing) monomial = invert(2,2,1) monomial == [0,1] Thus y_3 = y_{0,1} which delinearizes to x_0x_1
3. Supports dynamic programming/memoized mode and brute force. To use memoized: run_SA(k = 2,n = 5,A = A,b = b,memoize = True)