def infer_domain(f, gts, eqs, check_feas=True):
"""
Identify a subset of the constraints in ``gts`` and ``eqs`` which can be incorporated into
conditional SAGE relaxations for signomials. Construct a SigDomain object from the inferred constraints.
Parameters
----------
f : Signomial
The objective in a desired SAGE relaxation. This parameter is only used to determine
the dimension of the set defined by constraints in ``gts`` and ``eqs``.
gts : list of Signomials
For every ``g in gts``, there is a desired constraint that variables ``x`` satisfy ``g(x) >= 0``.
eqs : list of Signomials
For every ``g in eqs``, there is a desired constraint that variables ``x`` satisfy ``g(x) == 0``.
check_feas : bool
Indicates whether or not to verify that the returned SigDomain is nonempty.
Returns
-------
X : SigDomain or None
"""
conv_gt = con_gen.valid_posynomial_inequalities(gts)
conv_eqs = con_gen.valid_monomial_equations(eqs)
cl_cons = con_gen.clcons_from_standard_gprep(f.n, conv_gt, conv_eqs)
if len(cl_cons) > 0:
sigdom = SigDomain(f.n,
coniclifts_cons=cl_cons,
gts=conv_gt,
eqs=conv_eqs,
check_feas=check_feas)
return sigdom
else:
return None
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_infeasible_sig_domain(self):
x = cl.Variable()
cons = [x <= -1, x >= 1]
try:
dom = SigDomain(1, coniclifts_cons=cons)
assert False
except RuntimeError as err:
err_str = str(err)
assert 'seem to be infeasible' in err_str
A = np.ones(shape=(2, 2))
b = np.array([0, 1])
K = [cl.Cone('0', 2)]
try:
dom = SigDomain(2, AbK=(A, b, K))
assert False
except RuntimeError as err:
err_str = str(err)
assert 'seem to be infeasible' in err_str
pass