def test_slack(self):
b = np.abs(np.random.randn(*self.x.shape))
obj = sum_squares(self.x - b)
constr = [ChanceConstraint(self.x >= 0, 0.8)]
p = ccprob.Problem(Minimize(obj), constr)
p.solve(slack=False)
val_noslack = p.value
slacks = [cc.slack_value for cc in p.chance_constraints]
self.assertItemsAlmostEqual(slacks, len(p.chance_constraints) * [0])
p.solve(slack=True)
self.assertTrue(p.value <= val_noslack)
slacks = [cc.slack_value for cc in p.chance_constraints]
for slack in slacks:
self.assertAlmostGeq(slack, 0)
# Conflicting constraints: Prob(x <= 0) >= 0.2 and x >= 1.
constr += [self.x >= 1]
p = ccprob.Problem(Minimize(obj), constr)
with self.assertRaises(SolverError) as cm:
p.solve(slack=False)
# Solvable with slackened chance constraint.
p.solve(slack=True)
slacks = [cc.slack_value for cc in p.chance_constraints]
for slack in slacks:
self.assertAlmostGeq(slack, 0)
def test_dcp(self):
# Prob(g(x) >= 0) <= p is DCP iff g is convex.
constr = [ChanceConstraint(log(self.x) >= 0, 0.5)]
p = ccprob.Problem(Minimize(norm(self.x)), constr)
with self.assertRaises(DCPError) as cm:
p.solve()
# Prob(h(x) <= 0) <= p is DCP iff h is concave.
constr = [ChanceConstraint(exp(self.x) <= 5, 0.8)]
p = ccprob.Problem(Minimize(norm(self.x)), constr)
with self.assertRaises(DCPError) as cm:
p.solve()
def test_constraints(self):
obj = norm(self.x)
constr = [quantile(self.x, 0.6) <= -1]
p = ccprob.Problem(Minimize(obj), constr)
p.solve()
self.assertTrue(
np.sum(self.x.value <= -1 + self.tolerance) >= 0.6 * self.x.size)
b = np.abs(np.random.randn(self.x.size))
obj = norm(self.x - b)
constr = [quantile(self.x, 0.7) >= 1]
p = ccprob.Problem(Minimize(obj), constr)
p.solve()
self.assertTrue(
np.sum(self.x.value >= 1 - self.tolerance) >= np.round(1 - 0.7) *
self.x.size)
def test_solve(self):
b = np.abs(np.random.randn(*self.x.shape))
obj = sum_squares(self.x - b)
constr = [ChanceConstraint(self.x <= 0, 0.8)]
p = ccprob.Problem(Minimize(obj), constr)
p.solve()
self.assertTrue(
np.sum(self.x.value <= self.tolerance) <= 0.8 * self.x.size)
b = np.random.randn(self.A.shape[0])
obj = sum_squares(self.A * self.x - b)
constr = [ChanceConstraint(self.x >= 0, 0.8)]
p = ccprob.Problem(Minimize(obj), constr)
p.solve()
self.assertTrue(
np.sum(self.x.value >= -self.tolerance) <= 0.8 * self.x.size)
def test_2step(self):
b = np.abs(np.random.randn(*self.x.shape))
obj = sum_squares(self.x - b)
constr = [ChanceConstraint(self.x <= 0, 0.8)]
p = ccprob.Problem(Minimize(obj), constr)
p.solve(two_step=False)
val_1step = p.value
p.solve(two_step=True)
self.assertTrue(p.value <= val_1step)
def test_probability(self):
b = np.random.randn(self.A.shape[0])
obj = sum_squares(self.A * self.x - b)
cc = ChanceConstraint([self.x <= 0], 0.8)
pc = prob(self.x <= 0) <= 0.8
self.assertEqual(cc.size, pc.size)
self.assertEqual(cc.fraction, pc.fraction)
self.assertEqual(cc.max_violations, pc.max_violations)
self.assertAlmostEqual(
ccprob.Problem(Minimize(obj), [cc]).solve(),
ccprob.Problem(Minimize(obj), [pc]).solve())
cc = ChanceConstraint([self.x >= 0], 0.8)
pc = prob(self.x <= 0) >= 0.2
self.assertEqual(cc.size, pc.size)
self.assertEqual(cc.fraction, pc.fraction)
self.assertEqual(cc.max_violations, pc.max_violations)
self.assertAlmostEqual(
ccprob.Problem(Minimize(obj), [cc]).solve(),
ccprob.Problem(Minimize(obj), [pc]).solve())
def test_reduction_nested(self):
# Minimize 2*quantile(y, 0.5)) + 1
# subject to y >= 0.
t = Variable()
obj = 2 * t + 1
constr = [quantile(self.y, 0.5) <= t, self.y >= 0]
p0 = ccprob.Problem(Minimize(obj), constr)
p0.solve()
y_epi = self.y.value
obj = 2 * quantile(self.y, 0.5) + 1
constr = [self.y >= 0]
p1 = ccprob.Problem(Minimize(obj), constr)
p1.solve()
self.assertAlmostEqual(p1.value, p0.value)
self.assertItemsAlmostEqual(self.y.value, y_epi)
# Minimize -2*quantile(y, 0.75) + 3
# subject to y <= 5.
obj = -2 * t + 3
constr = [quantile(self.y, 0.75) >= t, self.y <= 5]
p0 = ccprob.Problem(Minimize(obj), constr)
p0.solve()
y_epi = self.y.value
obj = -2 * quantile(self.y, 0.75) + 3
constr = [self.y <= 5]
p1 = ccprob.Problem(Minimize(obj), constr)
p1.solve()
self.assertAlmostEqual(p1.value, p0.value)
self.assertItemsAlmostEqual(self.y.value, y_epi)
# Minimize quantile(y, 0.75) - quantile(y, 0.5)
u = Variable()
obj = t - u
constr = [
quantile(self.y, 0.75) <= t,
quantile(self.y, 0.5) >= u, self.y >= 0, self.y <= 1
]
p0 = ccprob.Problem(Minimize(obj), constr)
p0.solve()
y_epi = self.y.value
obj = quantile(self.y, 0.75) - quantile(self.y, 0.5)
constr = [self.y >= 0, self.y <= 1]
p1 = ccprob.Problem(Minimize(obj), constr)
p1.solve()
self.assertAlmostEqual(p1.value, p0.value)
self.assertItemsAlmostEqual(self.y.value, y_epi)
def test_reduction_basic(self):
# Minimize quantile(y, 0.5) subject to y >= 0.
t = Variable()
constr = [quantile(self.y, 0.5) <= t, self.y >= 0]
p0 = ccprob.Problem(Minimize(t), constr)
p0.solve()
y_epi = self.y.value
obj = quantile(self.y, 0.5)
constr = [self.y >= 0]
p1 = ccprob.Problem(Minimize(obj), constr)
p1.solve()
self.assertAlmostEqual(p1.value, p0.value)
self.assertItemsAlmostEqual(self.y.value, y_epi)
# Maximize quantile(y, 0.75) subject to y <= 5.
constr = [quantile(self.y, 0.75) >= t, self.y <= 5]
p0 = ccprob.Problem(Maximize(t), constr)
p0.solve()
y_epi = self.y.value
obj = quantile(self.y, 0.75)
constr = [self.y <= 5]
p1 = ccprob.Problem(Maximize(obj), constr)
p1.solve()
self.assertAlmostEqual(p1.value, p0.value)
self.assertItemsAlmostEqual(self.y.value, y_epi)
# Minimize quantile(abs(A*x - b), 0.5)
# subject to 0 <= x <= 1,
# quantile(x, 0.25) >= 0.1
b = np.random.randn(self.A.shape[0])
constr = [
quantile(abs(self.A * self.x - b), 0.5) <= t, self.x >= 0,
self.x <= 1,
quantile(self.x, 0.25) >= 0.1
]
p0 = ccprob.Problem(Minimize(t), constr)
p0.solve()
x_epi = self.x.value
obj = quantile(abs(self.A * self.x - b), 0.5)
constr = [self.x >= 0, self.x <= 1, quantile(self.x, 0.25) >= 0.1]
p1 = ccprob.Problem(Minimize(obj), constr)
p1.solve()
self.assertAlmostEqual(p1.value, p0.value)
self.assertItemsAlmostEqual(self.x.value, x_epi)