def create(m, n):
mu = 1
rho = 1
sigma = 0.1
A = problem_util.normalized_data_matrix(m, n, mu)
x0 = sp.rand(n, 1, rho)
x0.data = np.random.randn(x0.nnz)
x0 = x0.toarray().ravel()
b = np.sign(A.dot(x0) + sigma * np.random.randn(m))
A[b > 0, :] += 0.7 * np.tile([x0], (np.sum(b > 0), 1))
A[b < 0, :] -= 0.7 * np.tile([x0], (np.sum(b < 0), 1))
P = la.block_diag(np.random.randn(n - 1, n - 1), 0)
lam = 1
x = cp.Variable(A.shape[1])
# Straightforward formulation w/ no constraints
# TODO(mwytock): Fix compiler so this works
z0 = 1 - sp.diags([b], [0]) * A * x + cp.norm1(P.T * x)
f_eval = lambda: (lam * cp.sum_squares(x) + cp.sum_entries(
cp.max_elemwise(z0, 0))).value
# Explicit epigraph constraint
t = cp.Variable(1)
z = 1 - sp.diags([b], [0]) * A * x + t
f = lam * cp.sum_squares(x) + cp.sum_entries(cp.max_elemwise(z, 0))
C = [cp.norm1(P.T * x) <= t]
return cp.Problem(cp.Minimize(f), C), f_eval
def create(m, n):
mu = 1
rho = 1
sigma = 0.1
A = problem_util.normalized_data_matrix(m, n, mu)
x0 = sp.rand(n, 1, rho)
x0.data = np.random.randn(x0.nnz)
x0 = x0.toarray().ravel()
b = np.sign(A.dot(x0) + sigma*np.random.randn(m))
A[b>0,:] += 0.7*np.tile([x0], (np.sum(b>0),1))
A[b<0,:] -= 0.7*np.tile([x0], (np.sum(b<0),1))
P = la.block_diag(np.random.randn(n-1,n-1), 0)
lam = 1
x = cp.Variable(A.shape[1])
# Straightforward formulation w/ no constraints
# TODO(mwytock): Fix compiler so this works
z0 = 1 - sp.diags([b],[0])*A*x + cp.norm1(P.T*x)
f_eval = lambda: (lam*cp.sum_squares(x) + cp.sum_entries(cp.max_elemwise(z0, 0))).value
# Explicit epigraph constraint
t = cp.Variable(1)
z = 1 - sp.diags([b],[0])*A*x + t
f = lam*cp.sum_squares(x) + cp.sum_entries(cp.max_elemwise(z, 0))
C = [cp.norm1(P.T*x) <= t]
return cp.Problem(cp.Minimize(f), C), f_eval
def oneClassSVMProblem(problemOptions, solverOptions):
n = problemOptions['n']
m = problemOptions['m']
# Generate random points uniform over hypersphere
A = np.random.randn(m, n)
A /= np.sqrt(np.sum(A**2, axis=1))[:,np.newaxis] # Normalize each row of A
A *= (np.random.rand(m)**(1./n))[:,np.newaxis]
# Shift points and add some outliers
# NOTE(mwytock): causes problems for operator splitting, should fix
#x0 = np.random.randn(n)
x0 = np.zeros(n)
A += x0
k = max(m//50, 1)
idx = np.random.randint(0, m, k)
A[idx, :] += np.random.randn(k, n)
lam = 1
# Problem construction
x = cp.Variable(n)
rho = cp.Variable(1)
# Straightforward expression
z = np.sum(A**2, axis=1) - 2*A*x + cp.sum_squares(x) # z_i = ||a_i - x||^2
f = cp.sum_entries(cp.max_elemwise(z - rho, 0)) + lam*cp.sum_entries(cp.max_elemwise(0, rho))
prob = cp.Problem(cp.Minimize(f))
prob.solve(**solverOptions)
return {'Problem':prob, 'name':'oneClassSVMProblem'}
def create(m, n):
# Generate random points uniform over hypersphere
A = np.random.randn(m, n)
A /= np.sqrt(np.sum(A**2, axis=1))[:,np.newaxis]
A *= (np.random.rand(m)**(1./n))[:,np.newaxis]
# Shift points and add some outliers
# NOTE(mwytock): causes problems for operator splitting, should fix
#x0 = np.random.randn(n)
x0 = np.zeros(n)
A += x0
k = max(m/50, 1)
idx = np.random.randint(0, m, k)
A[idx, :] += np.random.randn(k, n)
lam = 1
x = cp.Variable(n)
rho = cp.Variable(1)
# Straightforward expression
#z = np.sum(A**2, axis=1) - 2*A*x + cp.sum_squares(x) # z_i = ||a_i - x||^2
#f = cp.sum_entries(cp.max_elemwise(z - rho, 0)) + lam*cp.max_elemwise(0, rho)
# Explicit epigraph form
t = cp.Variable(1)
z = np.sum(A**2, axis=1) - 2*A*x + t # z_i = ||a_i - x||^2
z0 = np.sum(A**2, axis=1) - 2*A*x + cp.sum_squares(x)
f_eval = lambda: ((1./n)*cp.sum_entries(cp.max_elemwise(z0 - rho, 0)) + cp.max_elemwise(0, rho)).value
f = (1./n)*cp.sum_entries(cp.max_elemwise(z-rho, 0)) + lam*cp.sum_entries(cp.max_elemwise(rho, 0))
C = [cp.sum_squares(x) <= t]
return cp.Problem(cp.Minimize(f), C), f_eval
def infinite_push(theta, Xp, Xn):
m, d = Xp.shape
n = Xn.shape[0]
Z = cp.max_elemwise(
1 - (Xp * theta * np.ones((1, n)) - (Xn * theta * np.ones((1, m))).T),
0)
return cp.max_entries(cp.sum_entries(Z, axis=0))
def create(**kwargs):
n = kwargs["n"]
x = cp.Variable(n)
u = np.random.rand(n)
f = cp.sum_squares(x-u)+cp.sum_entries(cp.max_elemwise(x, 0))
return cp.Problem(cp.Minimize(f))
def cost(self):
noload = cvx.Constant(self.no_load_cost)
if len(self.bid_curve) == 0: return noload
p = -self.terminals[0].power_var
offset = self.no_load_cost
segments = [offset + p * self.bid_curve[0][1]]
if len(self.bid_curve) == 1:
return segments[0]
offset += self.bid_curve[0][1] * self.bid_curve[0][0]
for i in range(len(self.bid_curve) - 1):
b = self.bid_curve[i + 1][1]
segments.append(b * (p - self.bid_curve[i][0]) + offset)
offset += b * (self.bid_curve[i + 1][0] - self.bid_curve[i][0])
return cvx.max_elemwise(*segments)
#gen = GeneratorWithBidCurve(
# no_load_cost=290.42,
# bid_curve=[
# (30, 21.21),
# (33.1, 21.43),
# (36.2, 21.66),
# (39.4, 21.93),
# (42.5, 22.22),
# (45.6, 22.53),
# (48.8, 22.87),
# (51.9, 23.22),
# (55, 23.6)])
#load = FixedLoad(power=43)
#net = Net([gen.terminals[0], load.terminals[0]])
#network = Group([gen, load], [net])
#print(network.optimize())
def envelope_fit(signal, mu, eta, kind='upper', period=None):
'''
Perform an envelope fit of a signal. See: https://en.wikipedia.org/wiki/Envelope_(waves)
:param signal: The signal to be fit
:param mu: A parameter to control the overall stiffness of the fit
:param eta: A parameter to control the permeability of the envelope. A large value result in
no data points outside the fitted envelope
:param kind: 'upper' or 'lower'
:return: An envelope signal of the same length as the input
'''
if kind == 'lower':
signal *= -1
n_samples = len(signal)
envelope = cvx.Variable(len(signal))
mu = cvx.Parameter(sign='positive', value=mu)
eta = cvx.Parameter(sign='positive', value=eta)
cost = (cvx.sum_entries(cvx.huber(envelope - signal)) +
mu * cvx.norm2(envelope[2:] - 2 * envelope[1:-1] + envelope[:-2]) +
eta * cvx.norm1(cvx.max_elemwise(signal - envelope, 0)))
objective = cvx.Minimize(cost)
if period is not None:
constraints = [envelope[:n_samples - period] == envelope[period:]]
problem = cvx.Problem(objective, constraints)
try:
problem.solve(solver='MOSEK')
except Exception as e:
print(e)
print('Trying ECOS solver')
problem.solve(solver='ECOS')
if kind == 'upper':
return envelope.value.A1
elif kind == 'lower':
signal *= -1
return -envelope.value.A1
def robustSVMProblem(problemOptions, solverOptions):
m = problemOptions['m']
n = problemOptions['n']
mu = problemOptions['mu']
rho = problemOptions['rho']
sigma = problemOptions['sigma']
gamma = problemOptions['gamma']
lam = problemOptions['lam']
A = __normalized_data_matrix(m, n, mu)
x0 = sps.rand(n, 1, rho)
x0.data = np.random.randn(x0.nnz)
x0 = x0.toarray().ravel()
b = np.sign(A.dot(x0) + sigma*np.random.randn(m))
A[b>0,:] += gamma*np.tile([x0], (np.sum(b>0),1))
A[b<0,:] -= gamma*np.tile([x0], (np.sum(b<0),1))
P = la.block_diag(np.random.randn(n-1,n-1), 0)
x = cp.Variable(n)
z = 1 - sps.diags([b],[0])*A*x + cp.norm1(P.T*x)
f = lam*cp.sum_squares(x) + cp.sum_entries(cp.max_elemwise(z, 0))
prob = cp.Problem(cp.Minimize(f))
prob.solve(**solverOptions)
return {'Problem':prob, 'name':'robustSVMProblem'}
def f_quantile_elemwise():
m = 4
k = 2
alphas = rand(k)
A = np.tile(alphas, (m, 1))
X = cp.Variable(m, k)
return cp.sum_entries(
cp.max_elemwise(cp.mul_elemwise(-A, X), cp.mul_elemwise(1 - A, X)))
def f_quantile_elemwise():
m = 4
k = 2
alphas = rand(k)
A = np.tile(alphas, (m, 1))
X = cp.Variable(m, k)
return cp.sum_entries(cp.max_elemwise(
cp.mul_elemwise( -A, X),
cp.mul_elemwise(1-A, X)))
def quantile_loss(alphas, Theta, X, y):
m, n = X.shape
k = len(alphas)
Y = np.tile(y, (k, 1)).T
A = np.tile(alphas, (m, 1))
Z = X*Theta - Y
return cp.sum_entries(
cp.max_elemwise(
cp.mul_elemwise( -A, Z),
cp.mul_elemwise(1-A, Z)))
def quantile_loss(alphas, Theta, X, y):
m, n = X.shape
k = len(alphas)
Y = np.tile(y.flatten(), (k, 1)).T
A = np.tile(alphas, (m, 1))
Z = X*Theta - Y
return cp.sum_entries(
cp.max_elemwise(
cp.mul_elemwise( -A, Z),
cp.mul_elemwise(1-A, Z)))
def cvx_loss_piecewise(self, d, a, b):
a_is_none = a is None
b_is_none = b is None
assert a_is_none or b_is_none
assert not (
a_is_none and b_is_none
), 'Constraint with both upper and lower bounds not implemented yet'
if not a_is_none:
v = [0, d]
elif not b_is_none:
v = [0, d]
return cvx.max_elemwise(*v)
def chebyshevProblem(problemOptions, solverOptions):
n = problemOptions['n']
m = problemOptions['m']
k = problemOptions['k']
A = [__normalized_data_matrix(m,n,1) for i in range(k)]
B = __normalized_data_matrix(k,n,1)
c = np.random.rand(k)
# Problem construction
x = cp.Variable(n)
obj_list = [cp.pnorm(A[i]*x, 2) + cp.abs(B[i,:]*x - c[i]) for i in range(k)]
f = cp.max_elemwise(obj_list)
prob = cp.Problem(cp.Minimize(f))
prob.solve(**solverOptions)
return {'Problem':prob, 'name':'chebyshevProblem'}
def cost(self):
p = -self.terminals[0].power_var
segments = [cvx.Constant(self.no_load_cost)]
prev_power = None
for power, price in self.bid_curve[1:]:
if prev_power is None:
offset = self.no_load_cost
else:
offset += (power - prev_power) * prev_price
segments.append(price * (p - power) + offset)
prev_power = power
prev_price = price
return cvx.max_elemwise(*segments)
def generate_cvx(cls, constraints, f, transform=None, scale=1.0):
x = np.zeros((len(constraints), constraints[0].x[0].size))
b = np.zeros(len(constraints))
for i, c in enumerate(constraints):
x_curr = c.x[0]
if transform is not None:
x_curr = transform.transform(x_curr)
x[i, :] = x_curr
b[i] = c.c[0]
if c.bound_type == BoundConstraint.BOUND_LOWER:
x[i, :] *= -1
b[i] *= -1
d = f(x) - b
#d = np.asarray(d)
#z = np.zeros((len(constraints)))
vals = cvx.max_elemwise(d, 0)
return cvx.sum_entries(vals)
def envelope_fit_with_deg(signal, period, mu, eta, kind='upper', eps=1e-4):
'''
Perform an approximately periodic envelope fit of a signal.
See: https://en.wikipedia.org/wiki/Envelope_(waves)
:param signal: The signal to be fit
:param mu: A parameter to control the overall stiffness of the fit
:param eta: A parameter to control the permeability of the envelope. A large value result in
no data points outside the fitted envelope
:param kind: 'upper' or 'lower'
:return: An envelope signal of the same length as the input
'''
offset_eps = False
if kind == 'lower':
signal *= -1
if np.min(signal) < 0:
print('function only works for signals with all values >= 0')
elif np.min(signal) == 0:
offset_eps = True
signal += eps
n_samples = len(signal)
beta = cvx.Variable()
envelope = cvx.Variable(len(signal))
mu = cvx.Parameter(sign='positive', value=mu)
eta = cvx.Parameter(sign='positive', value=eta)
cost = (cvx.sum_entries(cvx.huber(envelope - np.log(signal))) +
mu * cvx.norm2(envelope[2:] - 2 * envelope[1:-1] + envelope[:-2]) +
eta * cvx.norm1(cvx.max_elemwise(np.log(signal) - envelope, 0)))
objective = cvx.Minimize(cost)
constraints = [envelope[:n_samples - period] == envelope[period:] + beta]
problem = cvx.Problem(objective, constraints)
try:
problem.solve(solver='MOSEK')
#problem.solve()
except Exception as e:
print(e)
print('Trying ECOS solver')
problem.solve(solver='ECOS')
if offset_eps:
signal -= eps
if kind == 'upper':
return np.exp(envelope.value.A1), np.exp(beta.value)
elif kind == 'lower':
signal *= -1
return -np.exp(envelope.value.A1), np.exp(beta.value)
def to_cvx_dccp(constraints, f, logistic=False):
objective = 0
n = len(constraints)
t = cvx.Variable(n)
t_constraints = [0] * n
#d_far - d_close
for i, c in enumerate(constraints):
d_close, d_far = c.get_convex_terms(f)
'''
t_constraints[i] = t[i] == d_close
assert False, 'Is this correct?'
objective += cvx.max_elemwise(d_far - t[i], 0)
'''
t_constraints[i] = t[i] == d_far
if logistic:
objective += cvx.logistic(d_close - t[i])
else:
objective += cvx.max_elemwise(d_close - t[i], 0)
return objective, t, t_constraints
def cost(self):
if len(self.bid_curve) == 0: return cvx.Constant(0)
p = self.terminals[0].power_var
segments = [p * -self.bid_curve[0][1]]
if len(self.bid_curve) == 1:
return segments[0]
offset = -self.bid_curve[0][1] * self.bid_curve[0][0]
for i in range(len(self.bid_curve) - 1):
b = -self.bid_curve[i + 1][1]
segments.append(b * (p - self.bid_curve[i][0]) + offset)
offset += b * (self.bid_curve[i + 1][0] - self.bid_curve[i][0])
return cvx.max_elemwise(*segments)
#gen = GeneratorWithBidCurve(
# no_load_cost=290.42,
# bid_curve=[
# (30, 21.21),
# (33.1, 21.43),
# (36.2, 21.66),
# (39.4, 21.93),
# (42.5, 22.22),
# (45.6, 22.53),
# (48.8, 22.87),
# (51.9, 23.22),
# (55, 23.6)])
#fload = FixedLoad(32)
#load = LoadWithBidCurve(
# bid_curve=[
# (1, 33),
# (2, 32),
# (3, 30),
# (4, 28),
# (5, 25),
# (6, 24),
# (7, 23),
# (8, 22),
# (10, 20.9)], power_max=10)
#net = Net([gen.terminals[0], load.terminals[0], fload.terminals[0]])
#network = Group([gen, load, fload], [net])
#print(network.optimize())
def SVM_soft_L1(samples, labels, C):
"""
Input:
sample: np array in the format [[x1],[x2],....,[xn]] xi as col vectors
labels: np array [y1,y2,....,yn]
"""
t_in = time.time()
dim, Nsamples = samples.shape
theta = cvx.Variable(dim) # declaring dimension of variable
lam = 1 / C
Jump_term = cvx.max_elemwise(
0, 1 - cvx.mul_elemwise(labels, (theta.T @ samples).T))
Jump_term = cvx.sum_entries(Jump_term)
obj_expr = Jump_term + (lam / 2) * (cvx.sum_squares(theta[:-1]))
obj = cvx.Minimize(obj_expr)
prob = cvx.Problem(obj)
prob.solve(solver=cvx.ECOS)
theta_star = theta.value
theta_star = theta_star.tolist()
theta_star = [x[0] for x in theta_star]
print('SVM soft time ' + str(time.time() - t_in) + '\n')
return (theta_star)
def hinge_loss(theta, X, y):
if not all(np.unique(y) == [-1, 1]):
raise ValueError("y must have binary labels in {-1,1}")
return cp.sum_entries(
cp.max_elemwise(1 - sps.diags([y], [0]) * X * theta, 0))
def f_hinge():
return cp.sum_entries(cp.max_elemwise(x,0))
x0 = x0.toarray().ravel()
b = np.sign(A.dot(x0) + sigma * np.random.randn(m))
A[b > 0, :] += 0.7 * np.tile([x0], (np.sum(b > 0), 1))
A[b < 0, :] -= 0.7 * np.tile([x0], (np.sum(b < 0), 1))
P = la.block_diag(np.random.randn(n - 1, n - 1), 0)
lam = 1
# Problem construction
# Unconstrained formulation
x = cp.Variable(n)
z = 1 - sps.diags([b], [0]) * A * x + cp.norm1(P.T * x)
f = lam * cp.sum_squares(x) + cp.sum_entries(cp.max_elemwise(z, 0))
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))
prox("NON_NEGATIVE", None, lambda: [x >= 0]),
prox("NORM_1", f_norm1_weighted),
prox("NORM_1", lambda: cp.norm1(x)),
prox("NORM_2", lambda: cp.norm(X, "fro")),
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),
def hinge(x):
return cp.sum_entries(cp.max_elemwise(x,0))
def f_hinge_axis1():
return cp.sum_entries(cp.max_elemwise(X,0), axis=1)
def f_dead_zone():
eps = np.abs(randn())
return cp.sum_entries(cp.max_elemwise(cp.abs(x)-eps, 0))
import cvxpy as cp
x1 = cp.Variable(1)
x2 = cp.Variable(1)
constraints = [2*x1+x2 >= 1, x1+3*x2 >= 1, x1 >= 0, x2 >= 0]
objectives = [
cp.Minimize(x1 + x2),
cp.Minimize(-x1 - x2),
cp.Minimize(x1),
cp.Minimize(cp.max_elemwise(x1, x2)),
cp.Minimize(cp.power(x1, 2) + 9*cp.power(x2, 2))
]
for o_id, objective in enumerate(objectives):
prob = cp.Problem(objective, constraints)
print('< Objective', o_id, '>')
print('Optimal objective value :', prob.solve())
print('optimal value for variables: x1={}, x2={}'.format(x1.value, x2.value))
print('-------------------------------------------------------------------------\n')
def _estimate(self, t, wplus, z, value):
self.risks = [
risk.weight_expr(t, wplus, z, value) for risk in self.riskmodels
]
return cvx.max_elemwise(*self.risks)
def hinge_loss(theta, X, y):
return cp.sum_entries(cp.max_elemwise(1 - sp.diags([y],[0])*X*theta, 0))
def infinite_push(theta, Xp, Xn):
m, d = Xp.shape
n = Xn.shape[0]
Z = cp.max_elemwise(
1 - (Xp*theta*np.ones((1,n)) - (Xn*theta*np.ones((1,m))).T), 0)
return cp.max_entries(cp.sum_entries(Z, axis=0))
def f_dead_zone():
eps = np.abs(randn())
return cp.sum_entries(cp.max_elemwise(cp.abs(x)-eps, 0))
import cvxpy as cp, numpy as np, cvxopt, matplotlib.pyplot as plt
import ncvx
np.random.seed(1)
N = 41 # number of circles
r = 0.4 + 0.6 * np.random.rand(N) # radii
#define variables.
x_vals = [cp.Variable() for i in range(N)]
y_vals = [cp.Variable() for i in range(N)]
objective = cp.Minimize(cp.max_elemwise( *(x_vals + y_vals) ) + 0.5)
constraints = []
for i in range(N):
constraints += [0.5*r[i] <= x_vals[i],
0.5*r[i] <= y_vals[i]]
diff_vars = []
for i in range(N-1):
for j in range(i+1,N):
t = cp.Variable()
diff_vars.append(ncvx.Annulus(2, 0.5 * (r[i]+r[j]), N))
constraints += [
cp.vstack(x_vals[i] - x_vals[j],
y_vals[i] - y_vals[j]) == diff_vars[-1]]
prob = cp.Problem(objective, constraints)
result = prob.solve(method="relax-round-polish", polish_depth=100)
#plot the circles
circ = np.linspace(0,2 * np.pi)
np.random.seed(0)
m = 100
n = 200
k = 10
A = [normalized_data_matrix(m, n, 1) for i in range(k)]
B = normalized_data_matrix(k, n, 1)
c = np.random.rand(k)
# Problem construction
x = cp.Variable(n)
obj_list = [
cp.pnorm(A[i] * x, 2) + cp.abs(B[i, :] * x - c[i]) for i in range(k)
]
f = cp.max_elemwise(obj_list)
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()
def f_hinge_axis1():
return cp.sum_entries(cp.max_elemwise(X,0), axis=1)
x0 = np.zeros(n)
A += x0
k = max(m // 50, 1)
idx = np.random.randint(0, m, k)
A[idx, :] += np.random.randn(k, n)
lam = 1
# Problem construction
x = cp.Variable(n)
rho = cp.Variable(1)
# Straightforward expression
z = np.sum(A**2, axis=1) - 2 * A * x + cp.sum_squares(x) # z_i = ||a_i - x||^2
f = cp.sum_entries(cp.max_elemwise(
z - rho, 0)) + lam * cp.sum_entries(cp.max_elemwise(0, rho))
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))
han = []
mu = cvx.Parameter(sign='positive')
x = cvx.Variable(n, 1)
exp = pbar.T * x
var = cvx.quad_form(x, S)
obj = cvx.Minimize(-exp + mu * var)
cs1 = [npy.ones((1, n)) * x == 1]
prb = cvx.Problem(obj, [])
for idx in range(2):
if idx == 0:
prb.constraints = cs1 + [x >= 0]
lab = 'long only'
else:
prb.constraints = cs1 + \
[npy.ones((1, n)) * cvx.max_elemwise(-x, 0) <= .5]
lab = 'total short <= .5'
for jdx in range(nn):
mu.value = mus[jdx]
prb.solve()
#print(prb.status)
avg[jdx] = exp.value
std[jdx] = npy.sqrt(var.value)
#plot
hantemp = plt.plot(std, avg, label=lab)
han = han + hantemp
#plt.gca().set_aspect('equal')
ylimi = plt.gca().get_ylim()
plt.gca().set_ylim((0, ylimi[1]))
plt.ylabel('mean')
plt.xlabel('standard deviation')
prox("NORM_1", f_norm1_weighted),
prox("NORM_1", lambda: cp.norm1(x)),
prox("NORM_2", lambda: cp.norm(X, "fro")),
prox("NORM_2", lambda: cp.norm2(x)),
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),
def f_quantile():
alpha = rand()
return cp.sum_entries(cp.max_elemwise(alpha*x,(alpha-1)*x))
def hinge_loss(theta, X, y):
if not all(np.unique(y) == [-1, 1]):
raise ValueError("y must have binary labels in {-1,1}")
return cp.sum_entries(cp.max_elemwise(1 - sp.diags([y],[0])*X*theta, 0))
def f_quantile():
alpha = rand()
return cp.sum_entries(cp.max_elemwise(alpha*x,(alpha-1)*x))