def setUpClass(cls):
# test problem 1
G = np.array([[6, 2, 1], [2, 5, 2], [1, 2, 4]])
A = np.array([[1, 0, 1], [0, 1, 1]])
b = np.array([3, 0])
c = np.array([-8, -3, -3])
cls.model = create_basic_dense_qp(G, A, b, c)
cls.pyomo_nlp = PyomoNLP(cls.model)
cls.coupling_vars = [
cls.pyomo_nlp.variable_idx(cls.model.x[0]),
cls.pyomo_nlp.variable_idx(cls.model.x[2])
]
cls.nlp = AdmmNLP(cls.pyomo_nlp, cls.coupling_vars, rho=2.0)
# test problem 2
cls.model2 = create_model2()
cls.pyomo_nlp2 = PyomoNLP(cls.model2)
cls.coupling_vars2 = [
cls.pyomo_nlp2.variable_idx(cls.model2.x[1]),
cls.pyomo_nlp2.variable_idx(cls.model2.x[3]),
cls.pyomo_nlp2.variable_idx(cls.model2.x[5])
]
cls.nlp2 = AdmmNLP(cls.pyomo_nlp2, cls.coupling_vars2, rho=1.0)
# test problem 3
cls.model3 = create_basic_model()
cls.pyomo_nlp3 = PyomoNLP(cls.model3)
cls.coupling_vars3 = [cls.pyomo_nlp3.variable_idx(cls.model3.x[1])]
cls.nlp3 = AdmmNLP(cls.pyomo_nlp3, cls.coupling_vars3, rho=1.0)
def test_z_estimates(self):
z_estimates = np.array([5.0, 5.0])
nlp = AdmmNLP(self.pyomo_nlp,
self.coupling_vars,
rho=2.0,
z_estimates=z_estimates)
self.assertTrue(np.allclose(nlp.z_estimates, z_estimates))
z_estimates = np.array([6.0, 5.0])
nlp.z_estimates = z_estimates
self.assertTrue(np.allclose(nlp.z_estimates, z_estimates))
self.assertEqual(len(nlp.create_vector_z()), 2)
def test_objective(self):
w_estimates = np.array([5.0, 5.0])
z_estimates = np.array([2.0, 2.0])
rho = 2.0
nlp = AdmmNLP(self.pyomo_nlp,
self.coupling_vars,
rho=rho,
w_estimates=w_estimates,
z_estimates=z_estimates)
hessian_base = self.model.hessian_f
c = self.model.grad_f
A = np.array([[1, 0, 0], [0, 0, 1]], dtype=np.double)
x = nlp.create_vector_x()
x.fill(1.0)
f = 0.5 * x.transpose().dot(hessian_base.dot(x)) + c.dot(x)
difference = A.dot(x) - z_estimates
f += w_estimates.dot(difference)
f += 0.5 * rho * np.linalg.norm(difference)**2
self.assertEqual(f, nlp.objective(x))
def test_w_estimates(self):
w_estimates = np.array([5.0, 5.0])
nlp = AdmmNLP(self.pyomo_nlp,
self.coupling_vars,
rho=2.0,
w_estimates=w_estimates)
self.assertTrue(np.allclose(nlp.w_estimates(), w_estimates))
w_estimates = np.array([6.0, 5.0])
nlp.set_w_estimates(w_estimates)
self.assertTrue(np.allclose(nlp.w_estimates(), w_estimates))
self.assertEqual(len(nlp.create_vector_w()), 2)
def test_grad_objective(self):
w_estimates = np.array([5.0, 5.0])
z_estimates = np.array([2.0, 2.0])
rho = 2.0
nlp = AdmmNLP(self.pyomo_nlp,
self.coupling_vars,
rho=rho,
w_estimates=w_estimates,
z_estimates=z_estimates)
hessian_base = self.model.hessian_f
c = self.model.grad_f
A = np.array([[1, 0, 0], [0, 0, 1]], dtype=np.double)
x = nlp.create_vector_x()
x.fill(1.0)
df = hessian_base.dot(x) + c
df += A.transpose().dot(w_estimates)
df += rho * (A.transpose().dot(A).dot(x) -
A.transpose().dot(z_estimates))
self.assertTrue(np.allclose(df, nlp.grad_objective(x)))
def setUpClass(cls):
# test problem 1
G = np.array([[6, 2, 1], [2, 5, 2], [1, 2, 4]])
A = np.array([[1, 0, 1], [0, 1, 1]])
b = np.array([3, 0])
c = np.array([-8, -3, -3])
cls.model = create_basic_dense_qp(G, A, b, c)
cls.pyomo_nlp = PyomoNLP(cls.model)
cls.coupling_vars = [
cls.pyomo_nlp.variable_idx(cls.model.x[0]),
cls.pyomo_nlp.variable_idx(cls.model.x[2])
]
cls.nlp = AdmmNLP(cls.pyomo_nlp, cls.coupling_vars, rho=2.0)
def test_z_estimates(self):
z_estimates = np.array([5.0, 5.0])
nlp = AdmmNLP(self.pyomo_nlp,
self.coupling_vars,
rho=2.0,
z_estimates=z_estimates)
self.assertTrue(np.allclose(nlp.z_estimates(), z_estimates))
z_estimates = np.array([6.0, 5.0])
nlp.set_z_estimates(z_estimates)
self.assertTrue(np.allclose(nlp.z_estimates(), z_estimates))
self.assertEqual(len(nlp.create_vector_z()), 2)
def test_w_estimates(self):
w_estimates = np.array([5.0, 5.0])
nlp = AdmmNLP(self.pyomo_nlp,
self.coupling_vars,
rho=2.0,
w_estimates=w_estimates)
self.assertTrue(np.allclose(nlp.w_estimates(), w_estimates))
w_estimates = np.array([6.0, 5.0])
nlp.set_w_estimates(w_estimates)
self.assertTrue(np.allclose(nlp.w_estimates(), w_estimates))
self.assertEqual(len(nlp.create_vector_w()), 2)
def test_grad_objective(self):
w_estimates = np.array([5.0, 5.0])
z_estimates = np.array([2.0, 2.0])
rho = 2.0
nlp = AdmmNLP(self.pyomo_nlp,
self.coupling_vars,
rho=rho,
w_estimates=w_estimates,
z_estimates=z_estimates)
hessian_base = self.model.hessian_f
c = self.model.grad_f
A = np.array([[1, 0, 0], [0, 0, 1]], dtype=np.double)
x = nlp.create_vector_x()
x.fill(1.0)
df = hessian_base.dot(x) + c
df += A.transpose().dot(w_estimates)
df += rho * (A.transpose().dot(A).dot(x) - A.transpose().dot(z_estimates))
self.assertTrue(np.allclose(df, nlp.grad_objective(x)))
# second nlp
w_estimates = np.array([1.0, 2.0, 3.0])
z_estimates = np.array([3.0, 4.0, 5.0])
nlp = AdmmNLP(self.pyomo_nlp2,
self.coupling_vars2,
rho=3.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model2
transform = AdmmModel()
aug_model = transform.create_using(m,
complicating_vars=[m.x[1], m.x[3], m.x[5]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=3.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
self.assertTrue(np.allclose(nlp.grad_objective(x), nl.grad_objective(x)))
# third nlp
w_estimates = np.array([1.0])
z_estimates = np.array([3.0])
nlp = AdmmNLP(self.pyomo_nlp3,
self.coupling_vars3,
rho=8.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model3
transform = AdmmModel()
aug_model = transform.create_using(m,
complicating_vars=[m.x[1]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=8.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
x.fill(1.0)
self.assertTrue(np.allclose(nlp.grad_objective(x), nl.grad_objective(x)))
def test_objective(self):
w_estimates = np.array([5.0, 5.0])
z_estimates = np.array([2.0, 2.0])
rho = 2.0
nlp = AdmmNLP(self.pyomo_nlp,
self.coupling_vars,
rho=rho,
w_estimates=w_estimates,
z_estimates=z_estimates)
hessian_base = self.model.hessian_f
c = self.model.grad_f
A = np.array([[1, 0, 0], [0, 0, 1]], dtype=np.double)
x = nlp.create_vector_x()
x.fill(1.0)
f = 0.5 * x.transpose().dot(hessian_base.dot(x)) + c.dot(x)
difference = A.dot(x) - z_estimates
f += w_estimates.dot(difference)
f += 0.5 * rho * np.linalg.norm(difference)**2
self.assertEqual(f, nlp.objective(x))
# second nlp
w_estimates = np.array([1.0, 2.0, 3.0])
z_estimates = np.array([3.0, 4.0, 5.0])
nlp = AdmmNLP(self.pyomo_nlp2,
self.coupling_vars2,
rho=5.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model2
transform = AdmmModel()
aug_model = transform.create_using(m,
complicating_vars=[m.x[1], m.x[3], m.x[5]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=5.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
self.assertAlmostEqual(nlp.objective(x), nl.objective((x)))
# third nlp
w_estimates = np.array([1.0])
z_estimates = np.array([3.0])
nlp = AdmmNLP(self.pyomo_nlp3,
self.coupling_vars3,
rho=7.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model3
transform = AdmmModel()
aug_model = transform.create_using(m,
complicating_vars=[m.x[1]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=7.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
self.assertAlmostEqual(nlp.objective(x), nl.objective((x)))
def test_hessian_lag(self):
hessian_base = self.model.hessian_f
ata = np.array([[1, 0, 0], [0, 0, 0], [0, 0, 1]], dtype=np.double)
rho = self.nlp.rho
admm_hessian = hessian_base + ata * rho
x = self.nlp.create_vector_x()
y = self.nlp.create_vector_y()
hess_lag = self.nlp.hessian_lag(x, y)
dense_hess_lag = hess_lag.todense()
self.assertTrue(np.allclose(dense_hess_lag, admm_hessian))
# second nlp
w_estimates = np.array([1.0, 2.0, 3.0])
z_estimates = np.array([3.0, 4.0, 5.0])
nlp = AdmmNLP(self.pyomo_nlp2,
self.coupling_vars2,
rho=7.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model2
transform = AdmmModel()
aug_model = transform.create_using(m,
complicating_vars=[m.x[1], m.x[3], m.x[5]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=7.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
y = nlp.create_vector_y()
hess_lag = nlp.hessian_lag(x, y)
dense_hess_lag = hess_lag.todense()
hess_lagp = nl.hessian_lag(x, y)
dense_hess_lagp = hess_lagp.todense()
self.assertTrue(np.allclose(dense_hess_lag, dense_hess_lagp))
# third nlp
w_estimates = np.array([1.0])
z_estimates = np.array([3.0])
nlp = AdmmNLP(self.pyomo_nlp3,
self.coupling_vars3,
rho=1.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model3
transform = AdmmModel()
aug_model = transform.create_using(m,
complicating_vars=[m.x[1]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=1.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
y = nlp.create_vector_y()
hess_lag = nlp.hessian_lag(x, y)
dense_hess_lag = hess_lag.todense()
hess_lagp = nl.hessian_lag(x, y)
dense_hess_lagp = hess_lagp.todense()
self.assertTrue(np.allclose(dense_hess_lag, dense_hess_lagp))
def test_grad_objective(self):
w_estimates = np.array([5.0, 5.0])
z_estimates = np.array([2.0, 2.0])
rho = 2.0
nlp = AdmmNLP(self.pyomo_nlp,
self.coupling_vars,
rho=rho,
w_estimates=w_estimates,
z_estimates=z_estimates)
hessian_base = self.model.hessian_f
c = self.model.grad_f
A = np.array([[1, 0, 0], [0, 0, 1]], dtype=np.double)
x = nlp.create_vector_x()
x.fill(1.0)
df = hessian_base.dot(x) + c
df += A.transpose().dot(w_estimates)
df += rho * (A.transpose().dot(A).dot(x) -
A.transpose().dot(z_estimates))
self.assertTrue(np.allclose(df, nlp.grad_objective(x)))
# second nlp
w_estimates = np.array([1.0, 2.0, 3.0])
z_estimates = np.array([3.0, 4.0, 5.0])
nlp = AdmmNLP(self.pyomo_nlp2,
self.coupling_vars2,
rho=3.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model2
transform = AdmmModel()
aug_model = transform.create_using(
m,
complicating_vars=[m.x[1], m.x[3], m.x[5]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=3.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
self.assertTrue(
np.allclose(nlp.grad_objective(x), nl.grad_objective(x)))
# third nlp
w_estimates = np.array([1.0])
z_estimates = np.array([3.0])
nlp = AdmmNLP(self.pyomo_nlp3,
self.coupling_vars3,
rho=8.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model3
transform = AdmmModel()
aug_model = transform.create_using(m,
complicating_vars=[m.x[1]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=8.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
x.fill(1.0)
self.assertTrue(
np.allclose(nlp.grad_objective(x), nl.grad_objective(x)))
def test_objective(self):
w_estimates = np.array([5.0, 5.0])
z_estimates = np.array([2.0, 2.0])
rho = 2.0
nlp = AdmmNLP(self.pyomo_nlp,
self.coupling_vars,
rho=rho,
w_estimates=w_estimates,
z_estimates=z_estimates)
hessian_base = self.model.hessian_f
c = self.model.grad_f
A = np.array([[1, 0, 0], [0, 0, 1]], dtype=np.double)
x = nlp.create_vector_x()
x.fill(1.0)
f = 0.5 * x.transpose().dot(hessian_base.dot(x)) + c.dot(x)
difference = A.dot(x) - z_estimates
f += w_estimates.dot(difference)
f += 0.5 * rho * np.linalg.norm(difference)**2
self.assertEqual(f, nlp.objective(x))
# second nlp
w_estimates = np.array([1.0, 2.0, 3.0])
z_estimates = np.array([3.0, 4.0, 5.0])
nlp = AdmmNLP(self.pyomo_nlp2,
self.coupling_vars2,
rho=5.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model2
transform = AdmmModel()
aug_model = transform.create_using(
m,
complicating_vars=[m.x[1], m.x[3], m.x[5]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=5.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
self.assertAlmostEqual(nlp.objective(x), nl.objective((x)))
# third nlp
w_estimates = np.array([1.0])
z_estimates = np.array([3.0])
nlp = AdmmNLP(self.pyomo_nlp3,
self.coupling_vars3,
rho=7.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model3
transform = AdmmModel()
aug_model = transform.create_using(m,
complicating_vars=[m.x[1]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=7.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
self.assertAlmostEqual(nlp.objective(x), nl.objective((x)))
def test_hessian_lag(self):
hessian_base = self.model.hessian_f
ata = np.array([[1, 0, 0], [0, 0, 0], [0, 0, 1]], dtype=np.double)
rho = self.nlp.rho
admm_hessian = hessian_base + ata * rho
x = self.nlp.create_vector_x()
y = self.nlp.create_vector_y()
hess_lag = self.nlp.hessian_lag(x, y)
dense_hess_lag = hess_lag.todense()
self.assertTrue(np.allclose(dense_hess_lag, admm_hessian))
# second nlp
w_estimates = np.array([1.0, 2.0, 3.0])
z_estimates = np.array([3.0, 4.0, 5.0])
nlp = AdmmNLP(self.pyomo_nlp2,
self.coupling_vars2,
rho=7.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model2
transform = AdmmModel()
aug_model = transform.create_using(
m,
complicating_vars=[m.x[1], m.x[3], m.x[5]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=7.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
y = nlp.create_vector_y()
hess_lag = nlp.hessian_lag(x, y)
dense_hess_lag = hess_lag.todense()
hess_lagp = nl.hessian_lag(x, y)
dense_hess_lagp = hess_lagp.todense()
self.assertTrue(np.allclose(dense_hess_lag, dense_hess_lagp))
# third nlp
w_estimates = np.array([1.0])
z_estimates = np.array([3.0])
nlp = AdmmNLP(self.pyomo_nlp3,
self.coupling_vars3,
rho=1.0,
w_estimates=w_estimates,
z_estimates=z_estimates)
m = self.model3
transform = AdmmModel()
aug_model = transform.create_using(m,
complicating_vars=[m.x[1]],
z_estimates=z_estimates,
w_estimates=w_estimates,
rho=1.0)
nl = PyomoNLP(aug_model)
x = nlp.create_vector_x()
y = nlp.create_vector_y()
hess_lag = nlp.hessian_lag(x, y)
dense_hess_lag = hess_lag.todense()
hess_lagp = nl.hessian_lag(x, y)
dense_hess_lagp = hess_lagp.todense()
self.assertTrue(np.allclose(dense_hess_lag, dense_hess_lagp))