def _update(self):
with self.device:
if self.accelerate or self.proxg is not None:
backend.copyto(self.x_old, self.x)
if self.accelerate:
backend.copyto(self.x, self.z)
gradf_x = self.gradf(self.x)
util.axpy(self.x, -self.alpha, gradf_x)
if self.proxg is not None:
backend.copyto(self.x, self.proxg(self.alpha, self.x))
if self.accelerate:
t_old = self.t
self.t = (1 + (1 + 4 * t_old**2)**0.5) / 2
backend.copyto(
self.z,
self.x + (t_old - 1) / self.t * (self.x - self.x_old))
xp = self.device.xp
if self.accelerate or self.proxg is not None:
self.resid = util.asscalar(
xp.linalg.norm((self.x - self.x_old) / self.alpha**0.5))
else:
self.resid = util.asscalar(xp.linalg.norm(gradf_x))
def _update(self):
y = self.A(self.x)
device = backend.get_device(y)
xp = device.xp
with device:
self.max_eig = util.asscalar(xp.linalg.norm(y))
backend.copyto(self.x, y / self.max_eig)
def __init__(self, A, b, x, P=None, max_iter=100, tol=0):
self.A = A
self.P = P
self.x = x
self.tol = tol
self.device = backend.get_device(x)
with self.device:
xp = self.device.xp
self.r = b - self.A(self.x)
if self.P is None:
z = self.r
else:
z = self.P(self.r)
if max_iter > 1:
self.p = z.copy()
else:
self.p = z
self.not_positive_definite = False
self.rzold = xp.real(xp.vdot(self.r, z))
self.resid = util.asscalar(self.rzold)**0.5
super().__init__(max_iter)
def objective(self):
with self.y_device:
r = self.A(self.x) - self.y
obj = 1 / 2 * util.norm2(r)
if self.lamda > 0:
if self.R is None:
obj += self.lamda / 2 * util.norm2(self.x)
else:
obj += self.lamda / 2 * util.norm2(self.R(self.x))
if self.mu != 0:
obj += self.mu / 2 * util.norm2(self.x - self.z)
if self.proxg is not None:
if self.g is None:
raise ValueError(
'Cannot compute objective when proxg is specified,'
'but g is not.')
if self.G is None:
obj += self.g(self.x)
else:
obj += self.g(self.G(self.x))
obj = util.asscalar(obj)
return obj
def _update(self):
backend.copyto(self.u_old, self.u)
backend.copyto(self.x_old, self.x)
# Update dual.
delta_u = self.A(self.x_ext)
util.axpy(self.u, self.sigma, delta_u)
backend.copyto(self.u, self.proxfc(self.sigma, self.u))
# Update primal.
with self.x_device:
delta_x = self.AH(self.u)
if self.gradh is not None:
delta_x += self.gradh(self.x)
util.axpy(self.x, -self.tau, delta_x)
backend.copyto(self.x, self.proxg(self.tau, self.x))
# Update step-size if neccessary.
if self.gamma_primal > 0 and self.gamma_dual == 0:
with self.x_device:
xp = self.x_device.xp
theta = 1 / (
1 + 2 * self.gamma_primal * xp.amin(xp.abs(self.tau)))**0.5
self.tau *= theta
with self.u_device:
self.sigma /= theta
elif self.gamma_primal == 0 and self.gamma_dual > 0:
with self.u_device:
xp = self.u_device.xp
theta = 1 / (
1 + 2 * self.gamma_dual * xp.amin(xp.abs(self.sigma)))**0.5
self.sigma *= theta
with self.x_device:
self.tau /= theta
else:
theta = self.theta
# Extrapolate primal.
with self.x_device:
xp = self.x_device.xp
x_diff = self.x - self.x_old
backend.copyto(self.x_ext, self.x + theta * x_diff)
x_diff_norm = xp.linalg.norm(x_diff / self.tau**0.5)
with self.u_device:
xp = self.u_device.xp
u_diff = self.u - self.u_old
u_diff_norm = xp.linalg.norm(u_diff / self.sigma**0.5)
self.resid = util.asscalar(x_diff_norm**2 + u_diff_norm**2)
def _update(self):
xp = self.device.xp
with self.device:
if self.accelerate:
backend.copyto(self.x, self.z)
# Perform update
gradf_x = self.gradf(self.x)
alpha = self.alpha
x_new = self.x - alpha * gradf_x
if self.proxg is not None:
x_new = self.proxg(alpha, x_new)
delta_x = x_new - self.x
# Backtracking line search
if self.beta < 1:
fx = self.f(self.x)
while self.f(x_new) > fx + util.asscalar(
xp.real(xp.vdot(delta_x, gradf_x))) + \
1 / (2 * alpha) * util.asscalar(
xp.linalg.norm(delta_x))**2:
alpha *= self.beta
x_new = self.x - alpha * gradf_x
if self.proxg is not None:
x_new = self.proxg(alpha, x_new)
delta_x = x_new - self.x
backend.copyto(self.x, x_new)
if self.accelerate:
t_old = self.t
self.t = (1 + (1 + 4 * t_old**2)**0.5) / 2
backend.copyto(self.z,
x_new + ((t_old - 1) / self.t) * delta_x)
self.resid = util.asscalar(xp.linalg.norm(delta_x / alpha))
def _update(self):
with self.device:
xp = self.device.xp
Ap = self.A(self.p)
pAp = util.asscalar(xp.real(xp.vdot(self.p, Ap)))
if pAp <= 0:
self.not_positive_definite = True
return
self.alpha = self.rzold / pAp
util.axpy(self.x, self.alpha, self.p)
if self.iter < self.max_iter - 1:
util.axpy(self.r, -self.alpha, Ap)
if self.P is not None:
z = self.P(self.r)
else:
z = self.r
rznew = xp.real(xp.vdot(self.r, z))
beta = rznew / self.rzold
util.xpay(self.p, beta, z)
self.rzold = rznew
self.resid = util.asscalar(self.rzold)**0.5
def _update(self):
device = backend.get_device(self.x)
xp = device.xp
with device:
gradf_x = self.gradf(self.x)
p = -self.inv_hessf(self.x)(gradf_x)
self.lamda2 = util.asscalar(-xp.real(xp.vdot(p, gradf_x)))
if self.lamda2 < 0:
raise ValueError('Hessian is not positive semi-definite. '
'inv_hessf might not be defined correctly.')
x_new = self.x + p
if self.beta < 1:
fx = self.f(self.x)
alpha = 1
while self.f(x_new) > fx - alpha / 2 * self.lamda2:
alpha *= self.beta
x_new = self.x + alpha * p
backend.copyto(self.x, x_new)
self.residual = self.lamda2**0.5
