ADMM: ADMM

In pbombina/ADMM: ADMM to solve dense submatrix problem

Description

Iteratively solves the convex optimization problem using ADMM.

Usage

ADMM(G, c, n, tau = 0.35, gamma = 0.75, opt_tol = 1e-04, maxiter,
  quiet = TRUE)

Arguments

G:	sampled binary matrix
c:	natural number used to calculate number of rows in dense submatrix
n:	number of columns in dense submatrix
gamma:	l_1 regularization parameter
tau:	penalty parameter for equality constraint violation
tol:	stopping tolerance in algorithm
maxiter:	maximum number of iterations of the algorithm to run
quiet:	toggles between displaying intermediate statistics

Details

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

Value

Rank one matrix with mn nonzero entries, matrix Y that is used to count the number of disagreements between G and X

pbombina/ADMM documentation built on Aug. 14, 2019, 11:30 a.m.