Description Usage Arguments Details Value
Iteratively solves the convex optimization problem using ADMM.
1 2 |
G |
sampled binary matrix |
m |
number of rows in dense submatrix |
n |
number of columns in dense submatrix |
tau |
penalty parameter for equality constraint violation |
gamma |
l_1 regularization parameter |
opt_tol |
stopping tolerance in algorithm |
maxiter |
maximum number of iterations of the algorithm to run |
quiet |
toggles between displaying intermediate statistics |
min |X|_* + gamma* |Y|_1 + 1_Omega_W (W) + 1_Omega_Q (Q) + 1_Omega_Z (Z)
s.t X - Y = 0, X = W, X = Z,
where Omega_W (W), Omega_Q (Q), Omega_Z (Z) are the sets: Omega_W = {W in R^MxN | e^TWe = mn}
Omega_Q = {Q in R^MxN | Projection of Q on not N = 0}
Omega_Z = {Z in R^MxN | Z_ij <= 1 for all (i,j) in M x N}
Omega_Q = {Q in R^MxN | Projection of Q on not N = 0}
Omega_Z = {Z in R^MxN | Z_ij <= 1 for all (i,j) in M x N}
1_S is the indicator function of the set S in R^MxN such that 1_S(X) = 0 if X in S and +infinity otherwise
Rank one matrix with mn nonzero entries, matrix Y that is used to count the number of disagreements between G and X
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