def test_value_at_risk(self):
# Create problem data.
n = numpy.random.randint(1,10)
pbar = numpy.random.randn(n)
Sigma = numpy.eye(n)
p = NormalRandomVariable(pbar,Sigma)
o = numpy.ones((n,1))
beta = 0.05
num_samples = 50
# Create and solve optimization problem.
x = Variable(n)
p1 = Problem(Minimize(-x.T*pbar), [prob(-x.T*p >= 0, num_samples) <= beta, x.T*o == 1, x >= -0.1])
p1.solve()
# Create and solve analytic form of optimization problem (as a check).
p2 = Problem(Minimize(-x.T*pbar),
[x.T*pbar >= scipy.stats.norm.ppf(1-beta) * norm2(sqrtm(Sigma) * x), x.T*o == 1, x >= -0.1])
p2.solve()
tol = 0.1
if numpy.abs(p1.value - p2.value) < tol:
self.assertAlmostEqual(1,1)
else:
self.assertAlmostEqual(1,0)
def test_robust_svm(self):
# Create problem data.
m = 100 # num train points
m_pos = math.floor(m/2)
m_neg = m - m_pos
n = 2 # num dimensions
mu_pos = 2*numpy.ones(n)
mu_neg = -2*numpy.ones(n)
sigma = 1
X = numpy.matrix(numpy.vstack((mu_pos + sigma*numpy.random.randn(m_pos,n),
mu_neg + sigma*numpy.random.randn(m_neg,n))))
y = numpy.hstack((numpy.ones(m_pos), -1*numpy.ones(m_neg)))
C = 1 # regularization trade-off parameter
ns = 50
eta = 0.1
# Create and solve optimization problem.
w, b, xi = Variable(n), Variable(), NonNegative(m)
constr = []
Sigma = 0.1*numpy.eye(n)
for i in range(m):
mu = numpy.array(X[i])[0]
x = NormalRandomVariable(mu, Sigma)
chance = prob(-y[i]*(w.T*x+b) >= (xi[i]-1), ns)
constr += [chance <= eta]
p = Problem(Minimize(norm(w,2) + C*sum_entries(xi)),
constr)
p.solve(verbose=True)
w_new = w.value
b_new = b.value
# Create and solve the canonical SVM problem.
constr = []
for i in range(m):
constr += [y[i]*(X[i]*w+b) >= (1-xi[i])]
p2 = Problem(Minimize(norm(w,2) + C*sum_entries(xi)), constr)
p2.solve()
w_old = w.value
b_old = b.value
self.assert_feas(p)
def test_yield_constr_cost_min(self):
# Create problem data.
n = 10
c = numpy.random.randn(n)
P, q, r = numpy.eye(n), numpy.random.randn(n), numpy.random.randn()
mu, Sigma = numpy.zeros(n), 0.1*numpy.eye(n)
omega = NormalRandomVariable(mu, Sigma)
m, eta = 100, 0.95
# Create and solve optimization problem.
x = Variable(n)
yield_constr = prob(quad_form(x+omega,P)
+ (x+omega).T*q + r >= 0, m) <= 1-eta
p = Problem(Minimize(x.T*c), [yield_constr])
p.solve()
self.assert_feas(p)
def test_yield_constr_cost_min(self):
# Create problem data.
n = 10
c = numpy.random.randn(n)
P, q, r = numpy.eye(n), numpy.random.randn(n), numpy.random.randn()
mu, Sigma = numpy.zeros(n), 0.1 * numpy.eye(n)
omega = NormalRandomVariable(mu, Sigma)
m, eta = 100, 0.95
# Create and solve optimization problem.
x = Variable(n)
yield_constr = prob(
quad_form(x + omega, P) + (x + omega).T * q + r >= 0, m) <= 1 - eta
p = Problem(Minimize(x.T * c), [yield_constr])
p.solve()
self.assert_feas(p)
def test_simple_problem(self):
# Create problem data.
n = numpy.random.randint(1,10)
eta = 0.95
num_samples = 10
c = numpy.random.rand(n,1)
mu = numpy.zeros(n)
Sigma = numpy.eye(n)
a = NormalRandomVariable(mu, Sigma)
b = numpy.random.randn()
# Create and solve optimization problem.
x = Variable(n)
p = Problem(Maximize(x.T*c), [prob(max_entries(x.T*a-b) >= 0, num_samples) <= 1-eta])
p.solve()
self.assert_feas(p)
def test_simple_problem(self):
# Create problem data.
n = numpy.random.randint(1, 10)
eta = 0.95
num_samples = 10
c = numpy.random.rand(n, 1)
mu = numpy.zeros(n)
Sigma = numpy.eye(n)
a = NormalRandomVariable(mu, Sigma)
b = numpy.random.randn()
# Create and solve optimization problem.
x = Variable(n)
p = Problem(
Maximize(x.T * c),
[prob(max_entries(x.T * a - b) >= 0, num_samples) <= 1 - eta])
p.solve()
self.assert_feas(p)
def test_value_at_risk(self):
# Create problem data.
n = numpy.random.randint(1, 10)
pbar = numpy.random.randn(n)
Sigma = numpy.eye(n)
p = NormalRandomVariable(pbar, Sigma)
o = numpy.ones((n, 1))
beta = 0.05
num_samples = 50
# Create and solve optimization problem.
x = cp.Variable(n)
p1 = cp.Problem(
cp.Minimize(-x.T * pbar),
[
prob(-x.T * p >= 0, num_samples) <= beta, x.T * o == 1,
x >= -0.1
],
)
p1.solve(solver=cp.ECOS)
# Create and solve analytic form of optimization problem (as a check).
p2 = cp.Problem(
cp.Minimize(-x.T * pbar),
[
x.T * pbar >=
scipy.stats.norm.ppf(1 - beta) * cp.norm2(sqrtm(Sigma) * x),
x.T * o == 1,
x >= -0.1,
],
)
p2.solve()
tol = 0.1
if numpy.abs(p1.value - p2.value) < tol:
self.assertAlmostEqual(1, 1)
else:
self.assertAlmostEqual(1, 0)