def test_simple_sage_1(self):
"""
Solve a simple SAGE relaxation for a signomial minimization problem.
Do this without resorting to "Signomial" objects.
"""
alpha = np.array([[0, 0],
[1, 0],
[0, 1],
[1, 1],
[0.5, 0],
[0, 0.5]])
gamma = cl.Variable(shape=(), name='gamma')
c = cl.Expression([0 - gamma, 3, 2, 1, -4, -2])
expected_val = -1.8333331773244161
# with presolve
cl.presolve_trivial_age_cones(True)
con = cl.PrimalSageCone(c, alpha, None, 'test_con_name')
obj = gamma
prob = Problem(cl.MAX, obj, [con])
status, val = prob.solve(solver='ECOS', verbose=False)
assert abs(val - expected_val) < 1e-6
v = con.violation()
assert v < 1e-6
# without presolve
cl.presolve_trivial_age_cones(False)
con = cl.PrimalSageCone(c, alpha, None, 'test_con_name')
obj = gamma
prob = Problem(cl.MAX, obj, [con])
status, val = prob.solve(solver='ECOS', verbose=False)
assert abs(val - expected_val) < 1e-6
v = con.violation()
assert v < 1e-6
def test_unconstrained_sage_1(self, presolve=False, compactdual=True, kernel_basis=False):
# Background
#
# This is Example 1 from a 2018 paper by Murray, Chandrasekaran, and Wierman
# (https://arxiv.org/pdf/1810.01614.pdf).
#
# Tests
#
# (1) Check that primal / dual objectives are close to a reference values, for ell \in {0, 1}.
#
# (2) Recover a globally optimal solution at ell == 1.
#
initial_presolve = sage_cones.SETTINGS['presolve_trivial_age_cones']
initial_compactdual = sage_cones.SETTINGS['compact_dual']
initial_kb = sage_cones.SETTINGS['kernel_basis']
cl.presolve_trivial_age_cones(presolve)
cl.compact_sage_duals(compactdual)
cl.kernel_basis_age_witnesses(kernel_basis)
alpha = np.array([[0, 0],
[1, 0],
[0, 1],
[1, 1],
[0.5, 0],
[0, 0.5]])
c = np.array([0, 3, 2, 1, -4, -2])
s = Signomial(alpha, c)
expected = [-1.83333, -1.746505595]
pd0, _ = primal_dual_vals(s, 0)
self.assertAlmostEqual(pd0[0], expected[0], 4)
self.assertAlmostEqual(pd0[1], expected[0], 4)
pd1, dual = primal_dual_vals(s, 1)
self.assertAlmostEqual(pd1[0], expected[1], 4)
self.assertAlmostEqual(pd1[1], expected[1], 4)
optsols = sig_solrec(dual)
assert (s(optsols[0]) - dual.value) < 1e-6
cl.presolve_trivial_age_cones(initial_presolve)
cl.compact_sage_duals(initial_compactdual)
cl.kernel_basis_age_witnesses(initial_kb)
def test_unconstrained_sage_4(self, presolve=False, compactdual=False, kernel_basis=False):
# Background
#
# This example was constructed soley as a test case for sageopt.
#
# Minimize s(x) = exp(3*x) - 4*exp(2*x) + 7*exp(x) + exp(-x), over x \in R.
#
# Tests
#
# (1) Check that primal / dual objectives are close to reference values, for ell \in {0, 1, 2}.
#
# (2) Recover a globally optimal solution from the dual relaxation, when ell == 3.
#
# Notes
#
# It may not be obvious, but the signomial "s" is actually convex!
#
initial_presolve = sage_cones.SETTINGS['presolve_trivial_age_cones']
initial_compactdual = sage_cones.SETTINGS['compact_dual']
initial_kb = sage_cones.SETTINGS['kernel_basis']
cl.presolve_trivial_age_cones(presolve)
cl.compact_sage_duals(compactdual)
cl.kernel_basis_age_witnesses(kernel_basis)
s = Signomial.from_dict({(3,): 1, (2,): -4, (1,): 7, (-1,): 1})
expected = [3.464102, 4.60250026, 4.6217973]
pds = [primal_dual_vals(s, ell) for ell in range(3)]
for ell in range(3):
assert abs(pds[ell][0][0] - expected[ell]) < 1e-5
assert abs(pds[ell][0][1] - expected[ell]) < 1e-5
dual = sig_relaxation(s, form='dual', ell=3)
dual.solve(solver='ECOS', verbose=False)
optsols = sig_solrec(dual)
assert s(optsols[0]) < 1e-6 + dual.value
cl.presolve_trivial_age_cones(initial_presolve)
cl.compact_sage_duals(initial_compactdual)
cl.kernel_basis_age_witnesses(initial_kb)