def create(**kwargs):
# m>k
k = kwargs['k'] #class
m = kwargs['m'] #instance
n = kwargs['n'] #dim
p = 5 #p-largest
q = 10
X = problem_util.normalized_data_matrix(m,n,1)
Y = np.random.randint(0, k-1, (q,m))
Theta = cp.Variable(n,k)
t = cp.Variable(q)
texp = cp.Variable(m)
f = cp.sum_largest(t, p)+cp.sum_entries(texp) + cp.sum_squares(Theta)
C = []
C.append(cp.log_sum_exp(X*Theta, axis=1) <= texp)
for i in range(q):
Yi = one_hot(Y[i], k)
C.append(-cp.sum_entries(cp.mul_elemwise(X.T.dot(Yi), Theta)) == t[i])
t_eval = lambda: np.array([
-cp.sum_entries(cp.mul_elemwise(X.T.dot(one_hot(Y[i], k)), Theta)).value for i in range(q)])
f_eval = lambda: cp.sum_largest(t_eval(), p).value \
+ cp.sum_entries(cp.log_sum_exp(X*Theta, axis=1)).value \
+ cp.sum_squares(Theta).value
return cp.Problem(cp.Minimize(f), C), f_val
def create(**kwargs):
# m>k
k = kwargs['k'] #class
m = kwargs['m'] #instance
n = kwargs['n'] #dim
p = 5 #p-largest
X = problem_util.normalized_data_matrix(m, n, 1)
Y = np.random.randint(0, k, m)
Theta = cp.Variable(n, k)
t = cp.Variable(1)
texp = cp.Variable(m)
f = t + cp.sum_largest(texp, p) + cp.sum_squares(Theta)
C = []
C.append(cp.log_sum_exp(X * Theta, axis=1) <= texp)
Yi = one_hot(Y, k)
C.append(-cp.sum_entries(cp.mul_elemwise(X.T.dot(Yi), Theta)) == t)
t_eval = lambda: \
-cp.sum_entries(cp.mul_elemwise(X.T.dot(one_hot(Y, k)), Theta)).value
f_eval = lambda: t_eval() \
+ cp.sum_largest(cp.log_sum_exp(X*Theta, axis=1), p).value \
+ cp.sum_squares(Theta).value
return cp.Problem(cp.Minimize(f), C), f_eval
def test_validation(self):
"""Test that complex arguments are rejected.
"""
x = Variable(complex=True)
with self.assertRaises(Exception) as cm:
(x >= 0)
self.assertEqual(str(cm.exception),
"Inequality constraints cannot be complex.")
with self.assertRaises(Exception) as cm:
cvx.quad_over_lin(x, x)
self.assertEqual(
str(cm.exception),
"The second argument to quad_over_lin cannot be complex.")
with self.assertRaises(Exception) as cm:
cvx.sum_largest(x, 2)
self.assertEqual(str(cm.exception),
"Arguments to sum_largest cannot be complex.")
x = Variable(2, complex=True)
for atom in [
cvx.geo_mean, cvx.log_sum_exp, cvx.max, cvx.entr, cvx.exp,
cvx.huber, cvx.log, cvx.log1p, cvx.logistic
]:
name = atom.__name__
with self.assertRaises(Exception) as cm:
print(name)
atom(x)
self.assertEqual(str(cm.exception),
"Arguments to %s cannot be complex." % name)
x = Variable(2, complex=True)
for atom in [cvx.maximum, cvx.kl_div]:
name = atom.__name__
with self.assertRaises(Exception) as cm:
print(name)
atom(x, x)
self.assertEqual(str(cm.exception),
"Arguments to %s cannot be complex." % name)
x = Variable(2, complex=True)
for atom in [cvx.inv_pos, cvx.sqrt, lambda x: cvx.power(x, .2)]:
with self.assertRaises(Exception) as cm:
atom(x)
self.assertEqual(str(cm.exception),
"Arguments to power cannot be complex.")
x = Variable(2, complex=True)
for atom in [cvx.harmonic_mean, lambda x: cvx.pnorm(x, .2)]:
with self.assertRaises(Exception) as cm:
atom(x)
self.assertEqual(str(cm.exception),
"pnorm(x, p) cannot have x complex for p < 1.")
def maxSoftMaxEpigraphProblem(problemOptions, solverOptions):
k = problemOptions['k'] #class
m = problemOptions['m'] #instances
n = problemOptions['n'] #dim
p = problemOptions['p'] #p-largest
X = __normalized_data_matrix(m,n,1)
Y = np.random.randint(0, k, m)
# Problem construction
def one_hot(y, k):
m = len(y)
return sps.coo_matrix((np.ones(m), (np.arange(m), y)), shape=(m, k)).todense()
Theta = cp.Variable(n,k)
beta = cp.Variable(1, k)
t = cp.Variable(m)
texp = cp.Variable(m)
f = cp.sum_largest(t+texp, p) + cp.sum_squares(Theta)
C = []
C.append(cp.log_sum_exp(X*Theta + np.ones((m, 1))*beta, axis=1) <= texp)
Yi = one_hot(Y, k)
C.append(t == cp.vstack([-(X[i]*Theta + beta)[Y[i]] for i in range(m)]))
prob = cp.Problem(cp.Minimize(f), C)
prob.solve(**solverOptions)
return {'Problem':prob, 'name':'maxSoftMaxEpigraphProblem'}
def test_eigval_atoms(self):
"""Test eigenvalue atoms.
"""
P = np.arange(9) - 2j*np.arange(9)
P = np.reshape(P, (3, 3))
P1 = np.conj(P.T).dot(P)/10 + np.eye(3)*.1
P2 = np.array([[10, 1j, 0], [-1j, 10, 0], [0, 0, 1]])
for P in [P1, P2]:
value = cvx.lambda_max(P).value
X = Variable(P.shape, complex=True)
prob = Problem(cvx.Minimize(cvx.lambda_max(X)), [X == P])
result = prob.solve(solver=cvx.SCS, eps=1e-6)
self.assertAlmostEqual(result, value, places=2)
eigs = np.linalg.eigvals(P).real
value = cvx.sum_largest(eigs, 2).value
X = Variable(P.shape, complex=True)
prob = Problem(cvx.Minimize(cvx.lambda_sum_largest(X, 2)), [X == P])
result = prob.solve(solver=cvx.SCS, eps=1e-8)
self.assertAlmostEqual(result, value, places=3)
self.assertItemsAlmostEqual(X.value, P, places=3)
value = cvx.sum_smallest(eigs, 2).value
X = Variable(P.shape, complex=True)
prob = Problem(cvx.Maximize(cvx.lambda_sum_smallest(X, 2)), [X == P])
result = prob.solve(solver=cvx.SCS, eps=1e-6)
self.assertAlmostEqual(result, value, places=3)
def expr_intersects(self, other, eps=1e3):
or_vars = Variable(shape=4,
boolean=True,
name='overlap_or({},{})'.format(
self.name, other.name))
or_vars2 = Variable(shape=4,
boolean=True,
name='overlap_or({},{})'.format(
self.name, other.name))
j_vars = Variable(2, boolean=True)
constraints = [
# overlaps
# 0 , 0 -> True
# 0 , 1 -> False
# 1 , 0 -> False
# 1 , 1 -> False
# Does not overlap main
self.right <= other.x + eps * or_vars[0],
other.right <= self.x + eps * or_vars[1],
self.top <= other.y + eps * or_vars[2],
other.top <= self.y + eps * or_vars[3],
sum(or_vars) <= 3,
# --- or ---
# overlaps main and overlaps cutout
self.b2.right <= other.x + eps * or_vars2[0],
other.right <= self.b2.x + eps * or_vars2[1],
self.b2.top <= other.y + eps * or_vars2[2],
other.top <= self.b2.y + eps * or_vars2[3],
sum(or_vars2) >= 2,
# if above(1) is met sum largest will
cvx.sum_largest(or_vars, 3) * j_vars
]
return constraints
def CVX_Slope(X_train, y_train, llambda, k_Slope, solver):
start_time = time.time()
N, P = X_train.shape
beta = cvx.Variable(P)
beta0 = cvx.Variable()
loss = cvx.sum(cvx.pos(1 - cvx.multiply(y_train, X_train * beta + beta0)))
reg1 = cvx.norm(beta, 1)
#for j in range(min(P-1, K_max)): reg2 += (lambda_arr[j]-lambda_arr[j+1]) * sum_largest(abs(beta), j+1)
reg2 = cvx.sum_largest(cvx.abs(beta), k_Slope)
prob = cvx.Problem(cvx.Minimize(loss + llambda * reg1 + llambda * reg2))
dict_solver = {'gurobi': cvx.GUROBI, 'ecos': cvx.ECOS}
prob.solve(solver=dict_solver[solver])
### Solution
support = np.where(np.round(beta.value, 6) != 0)[0]
print '\nLen support ' + solver + ' = ' + str(len(support))
### Obj val
obj_val = prob.value
print 'Obj value ' + solver + ' = ' + str(obj_val)
### Time stops
time_cvx = time.time() - start_time
print 'Time CVX ' + solver + ' = ' + str(round(time_cvx, 2))
def test_sum_largest(self) -> None:
"""Test sum_largest.
"""
expr = cp.sum_largest(self.A, 2)
self.A.value = [[4, 3], [2, 1]]
self.assertItemsAlmostEqual(expr.grad[self.A].toarray(), [1, 0, 1, 0])
self.A.value = [[1, 2], [3, 0.5]]
self.assertItemsAlmostEqual(expr.grad[self.A].toarray(), [0, 1, 1, 0])
def create(**kwargs):
m = kwargs["m"]
n = kwargs["n"]
k = kwargs["k"]
A = np.matrix(np.random.rand(m, n))
A -= np.mean(A, axis=0)
K = np.array([(A[i].T * A[i]).flatten() for i in xrange(m)])
sigma = cp.Variable(n, n)
t = cp.Variable(m)
tdet = cp.Variable(1)
f = cp.sum_largest(t + tdet, k)
z = K * cp.reshape(sigma, n * n, 1)
C = [-cp.log_det(sigma) <= tdet, t == z]
det_eval = lambda: -cp.log_det(sigma).value
z_eval = lambda: (K * cp.reshape(sigma, n * n, 1)).value
f_eval = lambda: cp.sum_largest(z_eval() + det_eval(), k).value
return cp.Problem(cp.Minimize(f), C), f_eval
def test_sum_largest(self):
"""Test the sum_largest atom and related atoms.
"""
with self.assertRaises(Exception) as cm:
cp.sum_largest(self.x, -1)
self.assertEqual(str(cm.exception),
"Second argument must be a positive integer.")
with self.assertRaises(Exception) as cm:
cp.lambda_sum_largest(self.x, 2.4)
self.assertEqual(str(cm.exception),
"First argument must be a square matrix.")
with self.assertRaises(Exception) as cm:
cp.lambda_sum_largest(Variable((2, 2)), 2.4)
self.assertEqual(str(cm.exception),
"Second argument must be a positive integer.")
with self.assertRaises(ValueError) as cm:
cp.lambda_sum_largest([[1, 2], [3, 4]], 2).value
self.assertEqual(str(cm.exception),
"Input matrix was not Hermitian/symmetric.")
# Test copy with args=None
atom = cp.sum_largest(self.x, 2)
copy = atom.copy()
self.assertTrue(type(copy) is type(atom))
# A new object is constructed, so copy.args == atom.args but copy.args
# is not atom.args.
self.assertEqual(copy.args, atom.args)
self.assertFalse(copy.args is atom.args)
self.assertEqual(copy.get_data(), atom.get_data())
# Test copy with new args
copy = atom.copy(args=[self.y])
self.assertTrue(type(copy) is type(atom))
self.assertTrue(copy.args[0] is self.y)
self.assertEqual(copy.get_data(), atom.get_data())
# Test copy with lambda_sum_largest, which is in fact an AddExpression
atom = cp.lambda_sum_largest(Variable((2, 2)), 2)
copy = atom.copy()
self.assertTrue(type(copy) is type(atom))
def create(**kwargs):
m = kwargs["m"]
n = kwargs["n"]
k = kwargs["k"]
A = np.matrix(np.random.rand(m,n))
A -= np.mean(A, axis=0)
K = np.array([(A[i].T*A[i]).flatten() for i in xrange(m)])
sigma = cp.Variable(n,n)
t = cp.Variable(m)
tdet = cp.Variable(1)
f = cp.sum_largest(t+tdet, k)
z = K*cp.reshape(sigma, n*n, 1)
C = [-cp.log_det(sigma) <= tdet, t == z]
det_eval = lambda: -cp.log_det(sigma).value
z_eval = lambda: (K*cp.reshape(sigma, n*n, 1)).value
f_eval = lambda: cp.sum_largest(z_eval()+det_eval(), k).value
return cp.Problem(cp.Minimize(f), C), f_eval
def test_paper_example_sum_largest(self):
self.skipTest("Enable test once sum_largest is implemented.")
x = cvxpy.Variable((4, ), pos=True)
x0, x1, x2, x3 = (x[0], x[1], x[2], x[3])
obj = cvxpy.Minimize(
cvxpy.sum_largest(
cvxpy.hstack(
[3 * x0**0.5 * x1**0.5, x0 * x1 + 0.5 * x1 * x3**3, x2]),
2))
constr = [x0 * x1 * x2 >= 16]
p = cvxpy.Problem(obj, constr)
# smoke test.
p.solve(SOLVER, gp=True)
def maxGaussianEpigraphProblem(problemOptions, solverOptions):
m = problemOptions['m']
n = problemOptions['n']
k = problemOptions['k']
A = np.matrix(np.random.rand(m,n))
A -= np.mean(A, axis=0)
K = np.array([(A[i].T*A[i]).flatten() for i in range(m)])
sigma_inv = cp.Variable(n, n) # Inverse covariance matrix
obs = cp.vstack([-cp.log_det(sigma_inv) + cp.trace(A[i].T*A[i]*sigma_inv) for i in range(m)])
f = cp.sum_largest(obs, k)
prob = cp.Problem(cp.Minimize(f))
prob.solve(**solverOptions)
return {'Problem':prob, 'name':'maxGaussianEpigraphProblem'}
def maxSoftMaxProblem(problemOptions, solverOptions):
k = problemOptions['k'] #class
m = problemOptions['m'] #instances
n = problemOptions['n'] #dim
p = problemOptions['p'] #p-largest
X = __normalized_data_matrix(m,n,1)
Y = np.random.randint(0, k, m)
# Problem construction
Theta = cp.Variable(n,k)
beta = cp.Variable(1,k)
obs = cp.vstack([-(X[i]*Theta + beta)[Y[i]] + cp.log_sum_exp(X[i]*Theta + beta) for i in range(m)])
prob = cp.Problem(cp.Minimize(cp.sum_largest(obs, p) + cp.sum_squares(Theta)))
prob.solve(**solverOptions)
return {'Problem':prob, 'name':'maxSoftMaxProblem'}
def maxGaussianProblem(problemOptions, solverOptions):
m = problemOptions['m']
n = problemOptions['n']
k = problemOptions['k']
A = np.matrix(np.random.rand(m,n))
A -= np.mean(A, axis=0)
K = np.array([(A[i].T*A[i]).flatten() for i in range(m)])
sigma_inv1 = cp.Variable(n,n) # Inverse covariance matrix
t = cp.Variable(m)
tdet = cp.Variable(1)
f = cp.sum_largest(t+tdet, k)
z = K*cp.reshape(sigma_inv1, n*n, 1)
C = [-cp.log_det(sigma_inv1) <= tdet, t == z]
prob = cp.Problem(cp.Minimize(f), C)
prob.solve(**solverOptions)
return {'Problem':prob, 'name':'maxGaussianProblem'}
# Problem construction
def one_hot(y, k):
m = len(y)
return sps.coo_matrix((np.ones(m), (np.arange(m), y)),
shape=(m, k)).todense()
Theta = cp.Variable(n, k)
beta = cp.Variable(1, k)
t = cp.Variable(m)
texp = cp.Variable(m)
f = cp.sum_largest(t + texp, p) + cp.sum_squares(Theta)
C = []
C.append(cp.log_sum_exp(X * Theta + np.ones((m, 1)) * beta, axis=1) <= texp)
Yi = one_hot(Y, k)
C.append(t == cp.vstack([-(X[i] * Theta + beta)[Y[i]] for i in range(m)]))
prob = cp.Problem(cp.Minimize(f), C)
# Problem collection
# Single problem collection
problemDict = {"problemID": problemID, "problem": prob, "opt_val": opt_val}
problems = [problemDict]
# For debugging individual problems:
if __name__ == "__main__":
def test_sum_largest(self):
self.skipTest("Enable test once sum_largest is implemented.")
x = cvxpy.Variable((4, ), pos=True)
obj = cvxpy.Minimize(cvxpy.sum_largest(x, 3))
constr = [x[0] * x[1] * x[2] * x[3] >= 16]
dgp = cvxpy.Problem(obj, constr)
dgp2dcp = cvxpy.reductions.Dgp2Dcp(dgp)
dcp = dgp2dcp.reduce()
dcp.solve(SOLVER)
dgp.unpack(dgp2dcp.retrieve(dcp.solution))
opt = 6.0
self.assertAlmostEqual(dgp.value, opt)
self.assertAlmostEqual((x[0] * x[1] * x[2] * x[3]).value, 16, places=2)
dgp._clear_solution()
dgp.solve(SOLVER, gp=True)
self.assertAlmostEqual(dgp.value, opt)
self.assertAlmostEqual((x[0] * x[1] * x[2] * x[3]).value, 16, places=2)
# An unbounded problem.
x = cvxpy.Variable((4, ), pos=True)
y = cvxpy.Variable(pos=True)
obj = cvxpy.Minimize(cvxpy.sum_largest(x, 3) * y)
constr = [x[0] * x[1] * x[2] * x[3] >= 16]
dgp = cvxpy.Problem(obj, constr)
dgp2dcp = cvxpy.reductions.Dgp2Dcp(dgp)
dcp = dgp2dcp.reduce()
opt = dcp.solve(SOLVER)
self.assertEqual(dcp.value, -float("inf"))
dgp.unpack(dgp2dcp.retrieve(dcp.solution))
self.assertAlmostEqual(dgp.value, 0.0)
self.assertAlmostEqual(dgp.status, "unbounded")
dgp._clear_solution()
dgp.solve(SOLVER, gp=True)
self.assertAlmostEqual(dgp.value, 0.0)
self.assertAlmostEqual(dgp.status, "unbounded")
# Another unbounded problem.
x = cvxpy.Variable(2, pos=True)
obj = cvxpy.Minimize(cvxpy.sum_largest(x, 1))
dgp = cvxpy.Problem(obj, [])
dgp2dcp = cvxpy.reductions.Dgp2Dcp(dgp)
dcp = dgp2dcp.reduce()
opt = dcp.solve(SOLVER)
self.assertEqual(dcp.value, -float("inf"))
dgp.unpack(dgp2dcp.retrieve(dcp.solution))
self.assertAlmostEqual(dgp.value, 0.0)
self.assertAlmostEqual(dgp.status, "unbounded")
dgp._clear_solution()
dgp.solve(SOLVER, gp=True)
self.assertAlmostEqual(dgp.value, 0.0)
self.assertAlmostEqual(dgp.status, "unbounded")
# Composition with posynomials.
x = cvxpy.Variable((4, ), pos=True)
obj = cvxpy.Minimize(
cvxpy.sum_largest(
cvxpy.hstack([
3 * x[0]**0.5 * x[1]**0.5,
x[0] * x[1] + 0.5 * x[1] * x[3]**3, x[2]
]), 2))
constr = [x[0] * x[1] >= 16]
dgp = cvxpy.Problem(obj, constr)
dgp2dcp = cvxpy.reductions.Dgp2Dcp(dgp)
dcp = dgp2dcp.reduce()
dcp.solve(SOLVER)
dgp.unpack(dgp2dcp.retrieve(dcp.solution))
# opt = 3 * sqrt(4) * sqrt(4) + (4 * 4 + 0.5 * 4 * epsilon) = 28
opt = 28.0
self.assertAlmostEqual(dgp.value, opt, places=2)
self.assertAlmostEqual((x[0] * x[1]).value, 16.0, places=2)
self.assertAlmostEqual(x[3].value, 0.0, places=2)
dgp._clear_solution()
dgp.solve(SOLVER, gp=True)
self.assertAlmostEqual(dgp.value, opt, places=2)
self.assertAlmostEqual((x[0] * x[1]).value, 16.0, places=2)
self.assertAlmostEqual(x[3].value, 0.0, places=2)
(lambda x: cp.norm(x, 2), tuple(), [v_np], Constant([3])),
(lambda x: cp.norm(x, "fro"), tuple(), [[[-1, 2],
[3,
-4]]], Constant([5.47722557])),
(lambda x: cp.norm(x, 1), tuple(), [v_np], Constant([5])),
(lambda x: cp.norm(x, 1), tuple(), [[[-1, 2], [3, -4]]], Constant([10])),
(lambda x: cp.norm(x, "inf"), tuple(), [v_np], Constant([2])),
(lambda x: cp.norm(x, "inf"), tuple(), [[[-1, 2], [3,
-4]]], Constant([4])),
(lambda x: cp.norm(x, "nuc"), tuple(), [[[2, 0], [0, 1]]], Constant([3])),
(lambda x: cp.norm(x, "nuc"), tuple(), [[[3, 4, 5], [6, 7, 8], [9, 10,
11]]],
Constant([23.173260452512931])),
(lambda x: cp.norm(x, "nuc"), tuple(), [[[3, 4, 5], [6, 7, 8]]],
Constant([14.618376738088918])),
(lambda x: cp.sum_largest(cp.abs(x), 3), tuple(), [[1, 2, 3, -4, -5]],
Constant([5 + 4 + 3])),
(lambda x: cp.mixed_norm(x, 1, 1), tuple(), [[[1, 2], [3, 4],
[5, 6]]], Constant([21])),
(lambda x: cp.mixed_norm(x, 1, 1), tuple(), [[[1, 2, 3],
[4, 5, 6]]], Constant([21])),
# (lambda x: mixed_norm(x, 2, 1), tuple(), [[[3, 1], [4, math.sqrt(3)]]],
# Constant([7])),
(lambda x: cp.mixed_norm(x, 1, 'inf'), tuple(), [[[1, 4],
[5,
6]]], Constant([10])),
(cp.pnorm, tuple(), [[1, 2, 3]], Constant([3.7416573867739413])),
(lambda x: cp.pnorm(x, 1), tuple(), [[1.1, 2, -3]], Constant([6.1])),
(lambda x: cp.pnorm(x, 2), tuple(), [[1.1, 2, -3]],
Constant([3.7696153649941531])),
(lambda x: cp.pnorm(x, 2, axis=0), (2, ), [[[1, 2], [3, 4]]],
k = 20 #class
m = 100 #instance
n = 50 #dim
p = 5 #p-largest
X = normalized_data_matrix(m, n, 1)
Y = np.random.randint(0, k, m)
# Problem construction
Theta = cp.Variable(n, k)
beta = cp.Variable(1, k)
obs = cp.vstack([
-(X[i] * Theta + beta)[Y[i]] + cp.log_sum_exp(X[i] * Theta + beta)
for i in range(m)
])
prob = cp.Problem(cp.Minimize(cp.sum_largest(obs, p) + cp.sum_squares(Theta)))
# Problem collection
# Single problem collection
problemDict = {"problemID": problemID, "problem": prob, "opt_val": opt_val}
problems = [problemDict]
# For debugging individual problems:
if __name__ == "__main__":
def printResults(problemID="", problem=None, opt_val=None):
print(problemID)
problem.solve()
print("\tstatus: {}".format(problem.status))
print("\toptimal value: {}".format(problem.value))
prox("NORM_2", lambda: cp.norm2(x)),
prox("NORM_NUCLEAR", lambda: cp.norm(X, "nuc")),
prox("SECOND_ORDER_CONE", None, C_soc_scaled),
prox("SECOND_ORDER_CONE", None, C_soc_scaled_translated),
prox("SECOND_ORDER_CONE", None, C_soc_translated),
prox("SECOND_ORDER_CONE", None, lambda: [cp.norm(X, "fro") <= t]),
prox("SECOND_ORDER_CONE", None, lambda: [cp.norm2(x) <= t]),
prox("SEMIDEFINITE", None, lambda: [X >> 0]),
prox("SUM_DEADZONE", f_dead_zone),
prox("SUM_EXP", lambda: cp.sum_entries(cp.exp(x))),
prox("SUM_HINGE", f_hinge),
prox("SUM_HINGE", lambda: cp.sum_entries(cp.max_elemwise(1-x, 0))),
prox("SUM_HINGE", lambda: cp.sum_entries(cp.max_elemwise(1-x, 0))),
prox("SUM_INV_POS", lambda: cp.sum_entries(cp.inv_pos(x))),
prox("SUM_KL_DIV", lambda: cp.sum_entries(cp.kl_div(p1,q1))),
prox("SUM_LARGEST", lambda: cp.sum_largest(x, 4)),
prox("SUM_LOGISTIC", lambda: cp.sum_entries(cp.logistic(x))),
prox("SUM_NEG_ENTR", lambda: cp.sum_entries(-cp.entr(x))),
prox("SUM_NEG_LOG", lambda: cp.sum_entries(-cp.log(x))),
prox("SUM_QUANTILE", f_quantile),
prox("SUM_QUANTILE", f_quantile_elemwise),
prox("SUM_SQUARE", f_least_squares_matrix),
prox("SUM_SQUARE", lambda: f_least_squares(20)),
prox("SUM_SQUARE", lambda: f_least_squares(5)),
prox("SUM_SQUARE", f_quad_form),
prox("TOTAL_VARIATION_1D", lambda: cp.tv(x)),
prox("ZERO", None, C_linear_equality),
prox("ZERO", None, C_linear_equality_matrix_lhs),
prox("ZERO", None, C_linear_equality_matrix_rhs),
prox("ZERO", None, C_linear_equality_multivariate),
prox("ZERO", None, C_linear_equality_multivariate2),
prox("NORM_NUCLEAR", lambda: cp.norm(X, "nuc")),
#prox("QUAD_OVER_LIN", lambda: cp.quad_over_lin(p, q1)),
prox("SECOND_ORDER_CONE", None, C_soc_scaled),
prox("SECOND_ORDER_CONE", None, C_soc_scaled_translated),
prox("SECOND_ORDER_CONE", None, C_soc_translated),
prox("SECOND_ORDER_CONE", None, lambda: [cp.norm(X, "fro") <= t]),
prox("SECOND_ORDER_CONE", None, lambda: [cp.norm2(x) <= t]),
prox("SEMIDEFINITE", None, lambda: [X >> 0]),
prox("SUM_DEADZONE", f_dead_zone),
prox("SUM_EXP", lambda: cp.sum_entries(cp.exp(x))),
prox("SUM_HINGE", f_hinge),
prox("SUM_HINGE", lambda: cp.sum_entries(cp.max_elemwise(1-x, 0))),
prox("SUM_HINGE", lambda: cp.sum_entries(cp.max_elemwise(1-x, 0))),
prox("SUM_INV_POS", lambda: cp.sum_entries(cp.inv_pos(x))),
prox("SUM_KL_DIV", lambda: cp.sum_entries(cp.kl_div(p1,q1))),
prox("SUM_LARGEST", lambda: cp.sum_largest(x, 4)),
prox("SUM_LOGISTIC", lambda: cp.sum_entries(cp.logistic(x))),
prox("SUM_NEG_ENTR", lambda: cp.sum_entries(-cp.entr(x))),
prox("SUM_NEG_LOG", lambda: cp.sum_entries(-cp.log(x))),
prox("SUM_QUANTILE", f_quantile),
prox("SUM_QUANTILE", f_quantile_elemwise),
prox("SUM_SQUARE", f_least_squares_matrix),
prox("SUM_SQUARE", lambda: f_least_squares(20)),
prox("SUM_SQUARE", lambda: f_least_squares(5)),
prox("SUM_SQUARE", f_quad_form),
prox("TOTAL_VARIATION_1D", lambda: cp.tv(x)),
prox("ZERO", None, C_linear_equality),
prox("ZERO", None, C_linear_equality_matrix_lhs),
prox("ZERO", None, C_linear_equality_matrix_rhs),
prox("ZERO", None, C_linear_equality_multivariate),
prox("ZERO", None, C_linear_equality_multivariate2),
np.random.seed(0)
m = 10
n = 10
k = 3
A = np.matrix(np.random.rand(m,n))
A -= np.mean(A, axis=0)
K = np.array([(A[i].T*A[i]).flatten() for i in range(m)])
# Problem construction
sigma_inv1 = cp.Variable(n,n) # Inverse covariance matrix
t = cp.Variable(m)
tdet = cp.Variable(1)
f = cp.sum_largest(t+tdet, k)
z = K*cp.reshape(sigma_inv1, n*n, 1)
C = [-cp.log_det(sigma_inv1) <= tdet, t == z]
prob = cp.Problem(cp.Minimize(f), C)
# Problem collection
# Single problem collection
problemDict = {
"problemID" : problemID,
"problem" : prob,
"opt_val" : opt_val
}
problems = [problemDict]
np.random.seed(0)
m = 10
n = 10
k = 3
A = np.matrix(np.random.rand(m, n))
A -= np.mean(A, axis=0)
K = np.array([(A[i].T * A[i]).flatten() for i in range(m)])
# Problem construction
sigma_inv = cp.Variable(n, n) # Inverse covariance matrix
obs = cp.vstack([
-cp.log_det(sigma_inv) + cp.trace(A[i].T * A[i] * sigma_inv)
for i in range(m)
])
f = cp.sum_largest(obs, k)
prob = cp.Problem(cp.Minimize(f))
# Problem collection
# Single problem collection
problemDict = {"problemID": problemID, "problem": prob, "opt_val": opt_val}
problems = [problemDict]
# For debugging individual problems:
if __name__ == "__main__":
def printResults(problemID="", problem=None, opt_val=None):
print(problemID)
problem.solve()
print("\tstatus: {}".format(problem.status))
(lambda x: cp.max(x, axis=1), (2,), [[[-5, 2], [-3, 1]]], Constant([-3, 2])),
(lambda x: cp.norm(x, 2), tuple(), [v_np], Constant([3])),
(lambda x: cp.norm(x, "fro"), tuple(), [[[-1, 2], [3, -4]]],
Constant([5.47722557])),
(lambda x: cp.norm(x, 1), tuple(), [v_np], Constant([5])),
(lambda x: cp.norm(x, 1), tuple(), [[[-1, 2], [3, -4]]],
Constant([7])),
(lambda x: cp.norm(x, "inf"), tuple(), [v_np], Constant([2])),
(lambda x: cp.norm(x, "inf"), tuple(), [[[-1, 2], [3, -4]]],
Constant([6])),
(lambda x: cp.norm(x, "nuc"), tuple(), [[[2, 0], [0, 1]]], Constant([3])),
(lambda x: cp.norm(x, "nuc"), tuple(), [[[3, 4, 5], [6, 7, 8], [9, 10, 11]]],
Constant([23.173260452512931])),
(lambda x: cp.norm(x, "nuc"), tuple(), [[[3, 4, 5], [6, 7, 8]]],
Constant([14.618376738088918])),
(lambda x: cp.sum_largest(cp.abs(x), 3), tuple(), [[1, 2, 3, -4, -5]], Constant([5 + 4 + 3])),
(lambda x: cp.mixed_norm(x, 1, 1), tuple(), [[[1, 2], [3, 4], [5, 6]]],
Constant([21])),
(lambda x: cp.mixed_norm(x, 1, 1), tuple(), [[[1, 2, 3], [4, 5, 6]]],
Constant([21])),
# (lambda x: mixed_norm(x, 2, 1), tuple(), [[[3, 1], [4, math.sqrt(3)]]],
# Constant([7])),
(lambda x: cp.mixed_norm(x, 1, 'inf'), tuple(), [[[1, 4], [5, 6]]],
Constant([10])),
(cp.pnorm, tuple(), [[1, 2, 3]], Constant([3.7416573867739413])),
(lambda x: cp.pnorm(x, 1), tuple(), [[1.1, 2, -3]], Constant([6.1])),
(lambda x: cp.pnorm(x, 2), tuple(), [[1.1, 2, -3]], Constant([3.7696153649941531])),
(lambda x: cp.pnorm(x, 2, axis=0), (2,),
[[[1, 2], [3, 4]]], Constant([math.sqrt(5), 5.]).T),
(lambda x: cp.pnorm(x, 2, axis=1), (2,),