def solve_sdp_program(W):
assert W.ndim == 2
assert W.shape[0] == W.shape[1]
W = W.copy()
n = W.shape[0]
W = expand_matrix(W)
with Model('gw_max_3_cut') as M:
W = Matrix.dense(W / 3.)
J = Matrix.ones(3*n, 3*n)
# variable
Y = M.variable('Y', Domain.inPSDCone(3*n))
# objective function
M.objective(ObjectiveSense.Maximize, Expr.dot(W, Expr.sub(J, Y)))
# constraints
for i in range(3*n):
M.constraint(f'c_{i}{i}', Y.index(i, i), Domain.equalsTo(1.))
for i in range(n):
M.constraint(f'c_{i}^01', Y.index(i*3, i*3+1), Domain.equalsTo(-1/2.))
M.constraint(f'c_{i}^02', Y.index(i*3, i*3+2), Domain.equalsTo(-1/2.))
M.constraint(f'c_{i}^12', Y.index(i*3+1, i*3+2), Domain.equalsTo(-1/2.))
for j in range(i+1, n):
for a, b in product(range(3), repeat=2):
M.constraint(f'c_{i}{j}^{a}{b}-0', Y.index(i*3 + a, j*3 + b), Domain.greaterThan(-1/2.))
M.constraint(f'c_{i}{j}^{a}{b}-1', Expr.sub(Y.index(i*3 + a, j*3 + b), Y.index(i*3 + (a + 1) % 3, j*3 + (b + 1) % 3)), Domain.equalsTo(0.))
M.constraint(f'c_{i}{j}^{a}{b}-2', Expr.sub(Y.index(i*3 + a, j*3 + b), Y.index(i*3 + (a + 2) % 3, j*3 + (b + 2) % 3)), Domain.equalsTo(0.))
# solution
M.solve()
Y_opt = Y.level()
return np.reshape(Y_opt, (3*n,3*n))
def solve_sdp_program(A):
assert A.ndim == 2
assert A.shape[0] == A.shape[1]
A = A.copy()
n = A.shape[0]
with Model('theta_1') as M:
A = Matrix.dense(A)
# variable
X = M.variable('X', Domain.inPSDCone(n))
# objective function
M.objective(ObjectiveSense.Maximize,
Expr.sum(Expr.dot(Matrix.ones(n, n), X)))
# constraints
M.constraint(f'c1', Expr.sum(Expr.dot(X, A)), Domain.equalsTo(0.))
M.constraint(f'c2', Expr.sum(Expr.dot(X, Matrix.eye(n))),
Domain.equalsTo(1.))
# solution
M.solve()
sol = X.level()
return sum(sol)
def solve_sdp_program(W):
assert W.ndim == 2
assert W.shape[0] == W.shape[1]
W = W.copy()
n = W.shape[0]
with Model('gw_max_cut') as M:
W = Matrix.dense(W / 4.)
J = Matrix.ones(n, n)
# variable
Y = M.variable('Y', Domain.inPSDCone(n))
# objective function
M.objective(ObjectiveSense.Maximize, Expr.dot(W, Expr.sub(J, Y)))
# constraints
for i in range(n):
M.constraint(f'c_{i}', Y.index(i, i), Domain.equalsTo(1.))
# solve
M.solve()
# solution
Y_opt = Y.level()
return np.reshape(Y_opt, (n, n))
def solve_sdp_program(W, k):
assert W.ndim == 2
assert W.shape[0] == W.shape[1]
W = W.copy()
n = W.shape[0]
with Model('fj_max_k_cut') as M:
W = Matrix.dense((k - 1) / (2 * k) * W)
J = Matrix.ones(n, n)
# variable
Y = M.variable('Y', Domain.inPSDCone(n))
# objective function
M.objective(ObjectiveSense.Maximize, Expr.dot(W, Expr.sub(J, Y)))
# constraints
for i in range(n):
M.constraint(f'c_{i}', Y.index(i, i), Domain.equalsTo(1.))
for j in range(i + 1, n):
M.constraint(f'c_{i},{j}', Y.index(i, j),
Domain.greaterThan(-1 / (k - 1)))
# solution
M.solve()
Y_opt = Y.level()
return np.reshape(Y_opt, (n, n))