def test_conditional_sage_dual_1(self):
n, m = 2, 6
x = Variable(shape=(n, ), name='x')
cons = [1 >= vector2norm(x)]
gts = [lambda z: 1 - np.linalg.norm(z, 2)]
eqs = []
sigdom = SigDomain(n, coniclifts_cons=cons, gts=gts, eqs=eqs)
np.random.seed(0)
x0 = np.random.randn(n)
x0 /= 2 * np.linalg.norm(x0)
alpha = np.random.randn(m, n)
c = np.array([1, 2, 3, 4, -0.5, -0.1])
v0 = np.exp(alpha @ x0)
v = Variable(shape=(m, ), name='projected_v0')
t = Variable(shape=(1, ), name='epigraph_var')
sage_constraint = sage_cones.DualSageCone(v,
alpha,
name='test',
X=sigdom,
c=c)
epi_constraint = vector2norm(v - v0) <= t
constraints = [sage_constraint, epi_constraint]
prob = Problem(CL_MIN, t, constraints)
prob.solve(solver='ECOS')
v0 = sage_constraint.violation(norm_ord=1, rough=False)
assert v0 < 1e-6
v1 = sage_constraint.violation(norm_ord=np.inf, rough=True)
assert v1 < 1e-6
val = prob.value
assert val < 1e-7
def test_ordinary_sage_dual_3(self):
# provide a vector "c" in the dual SAGE cone constructor.
# generate a point with zero distance from the dual SAGE cone
n, m = 2, 6
np.random.seed(0)
alpha = 10 * np.random.randn(m, n)
x0 = np.random.randn(n) / 10
v0 = np.exp(alpha @ x0)
dummy_vars = Variable(shape=(2, )).scalar_variables()
c = np.array([1, 2, 3, 4, dummy_vars[0], dummy_vars[1]])
c = Expression(c)
v = Variable(shape=(m, ), name='projected_v0')
t = Variable(shape=(1, ), name='epigraph_var')
sage_constraint = sage_cones.DualSageCone(v,
alpha,
X=None,
name='test_con',
c=c)
epi_constraint = vector2norm(v - v0) <= t
constraints = [sage_constraint, epi_constraint]
prob = Problem(CL_MIN, t, constraints)
prob.solve(solver='ECOS')
viol = sage_constraint.violation(norm_ord=1, rough=False)
assert viol < 1e-6
viol = sage_constraint.violation(norm_ord=np.inf, rough=True)
assert viol < 1e-6
val = prob.value
assert val < 1e-7
def test_ordinary_sage_dual_2(self):
# generate a point with zero distance from the dual SAGE cone
n, m = 2, 6
np.random.seed(0)
alpha = 10 * np.random.randn(m, n)
x0 = np.random.randn(n) / 10
v0 = np.exp(alpha @ x0)
v = Variable(shape=(m, ), name='projected_v0')
t = Variable(shape=(1, ), name='epigraph_var')
sage_constraint = sage_cones.DualSageCone(v,
alpha,
X=None,
name='test_con')
epi_constraint = vector2norm(v - v0) <= t
constraints = [sage_constraint, epi_constraint]
prob = Problem(CL_MIN, t, constraints)
prob.solve(solver='ECOS')
viol = sage_constraint.violation(norm_ord=1, rough=False)
assert viol < 1e-6
viol = sage_constraint.violation(norm_ord=np.inf, rough=True)
assert viol < 1e-6
val = prob.value
assert val < 1e-7
def test_ordinary_sage_dual_1(self):
# generate a point which has positive distance from the dual SAGE cone
n, m = 2, 6
np.random.seed(0)
alpha = 10 * np.random.randn(m, n)
v0 = 10 * np.abs(np.random.randn(m)) + 0.01
v0[0] = -v0[0]
v = Variable(shape=(m, ), name='projected_v0')
t = Variable(shape=(1, ), name='epigraph_var')
sage_constraint = sage_cones.DualSageCone(v,
alpha,
X=None,
name='test_con')
epi_constraint = vector2norm(v - v0) <= t
constraints = [sage_constraint, epi_constraint]
prob = Problem(CL_MIN, t, constraints)
prob.solve(solver='ECOS')
viol = sage_constraint.violation(norm_ord=1, rough=False)
assert viol < 1e-6
viol = sage_constraint.violation(norm_ord=np.inf, rough=True)
assert viol < 1e-6
val = prob.value
assert val + 1e-6 >= abs(v0[0])