def main():
#PGM:
'''
x = np.array([[1.]])
landa = 0.5
alpha = 0.1
A = np.array([[1.]])
b = np.array([[.2]])
error = 0.001
xx, count, obj = PGM(x, alpha, landa, A, b, error)
print(obj)
draw(obj)
'''
#ADMM
x = np.array([[1.]])
z = np.array([[1.]])
landa = np.array([[1.]])
A = np.array([[1.]])
b = np.array([[.2]])
alpha = 0.1
error = 0.01
beta = 0.01
xx, count, obj = ADMM(x, alpha, landa, A, b, error, beta, z)
draw(obj)
print("最终迭代结果: x：", xx)
print("共进行了", count, "次迭代")
def main():
#SD:
# x = np.array([[1.]])
# alpha=0.1
# landa=0.5
# A = np.array([[1.]])
# b = np.array([[.2]])
# error=0.0001
# xx,count,obj=SD(x,alpha,landa,A,b,error)
#BFGS:
# x = np.array([[1.]])
# xx = np.array([[1.4]])
# alpha=0.1
# epsi=0.3
# A = np.array([[1.]])
# b = np.array([[.2]])
# error=0.001
# D = np.array([[1.5]])
# xx,count,obj=BFGS(x,xx,A,b,alpha,D,epsi,error)
#ADMM
x = np.array([[1.]])
z = np.array([[1.]])
landa = np.array([[1.]])
A = np.array([[1.]])
b = np.array([[.2]])
alpha = 0.1
error = 0.01
beta = 0.01
xx, count, obj = ADMM(x, alpha, landa, A, b, error, beta, z)
draw(obj)
print("最终迭代结果: x：", xx)
print("共进行了", count, "次迭代")
def ADMM(A, b, alpha=0.1, beta=0.01, show_x=True, show_graph=True, log_int=1):
#ADMM(x, alpha, landa, A, b, error, beta, z):
n = A.shape[1]
x = np.random.rand(n, 1)
z = np.random.rand(n, 1)
landa = np.random.rand(n, 1)
k = 0
if show_x:
print("x starts with: ")
print(x)
red = np.linalg.norm(x, ord=1) + (alpha / 2) * np.linalg.norm(A @ x - b)**2
print('The initial target value is %f' % (red))
obj = []
p = random.uniform(1.5, 1.8)
I = np.identity(n)
zero = np.zeros(n)
zero = zero.T
while (1):
part_1 = np.linalg.inv(alpha * (A.T @ A) + beta * I)
part_2 = alpha * (A.T @ b) + beta * z - landa
xx = part_1 @ part_2
zz = (landa + beta * (xx * p - (1 - p) * z)) / (2 + beta)
landalanda = landa + beta * (p * xx - (1 - p) * z - zz)
red = np.linalg.norm(
xx, ord=1) + (alpha / 2) * np.linalg.norm(A @ xx - b)**2
if k % log_int == 0:
obj.append(red)
print('The %dth iteration, target value is %f' % (k, red))
'''
xzk = np.vstack((x, z))
xzkp = np.vstack((xx, zz))
e = np.linalg.norm(xzk - xzkp)
if e <= error:
break
'''
if stop(I, xx, -I, zz, z, zero, landalanda, alpha):
break
else:
x = np.copy(xx)
z = np.copy(zz)
landa = np.copy(landalanda)
if show_x:
print('The current x is: ', x)
k += 1
print("Final x: ", xx)
print("Total steps: ", k)
if show_graph:
draw(obj, log_int)
return xx, k, obj
def main():
x = np.array([[1.]])
z = np.array([[1.]])
landa = np.array([[1.]])
A = np.array([[1.]])
b = np.array([[.2]])
alpha = 0.1
beta = 0.01
D = np.array([[0.5]])
xx, count, obj = ADMM(x, alpha, landa, A, b, beta, z, D)
draw(obj)
print("最终迭代结果: x：", xx)
print("共进行了", count, "次迭代")
def PGM(A, b, alpha=0.1, error=0.001, show_x=True, show_graph=True, log_int=1):
k = 0
n = A.shape[1]
x = np.random.rand(n, 1)
landa = np.random.rand(n, 1)
if show_x:
print("x starts with: ")
print(x)
red = np.linalg.norm(x, ord=1) + (alpha / 2) * np.linalg.norm(A @ x - b)**2
print('The initial target value is %f' % (red))
obj = []
while (1):
z = x - alpha * landa * np.dot(A.T, np.dot(A, x) - b)
xx = np.copy(x)
xx = np.sign(z) * np.maximum(np.linalg.norm(z) - alpha, 0)
red = np.linalg.norm(
xx, ord=1) + (alpha / 2) * np.linalg.norm(A @ xx - b)**2
if k % log_int == 0:
obj.append(red)
if k % log_int == 0:
print('The %dth iteration, target value is %f' % (k, red))
e = np.linalg.norm(xx - x)
if e < error:
break
else:
x = np.copy(xx)
if show_x:
print('The current x is: ', x)
k += 1
print("Final x: ", xx)
print("Total steps: ", k)
if show_graph:
draw(obj, log_int)
return xx, k, obj
def BFGS(A,
b,
alpha=0.1,
epsi=0.3,
error=0.001,
show_x=True,
show_graph=True,
log_int=1):
k = 0
n = A.shape[1]
x = np.random.rand(n, 1)
xx = np.random.rand(n, 1)
D = np.random.rand(n, n)
if show_x:
print("x starts with: ")
print(x)
obj = []
while (1):
p = xx - x
delta_x = 2 * x + alpha * np.dot(A.T, np.dot(A, x) - b)
delta_xx = 2 * xx + alpha * np.dot(A.T, np.dot(A, x) - b)
q = delta_xx - delta_x
tao = q.T @ D @ q
temp1 = p / np.dot(p.T, q)
temp2 = np.dot(D, q) / tao
v = temp1 - temp2
part_2 = np.dot(p, p.T) / np.dot(p, q.T)
part_3 = np.dot(np.dot(np.dot(D, q), q.T), D.T) / np.dot(
np.dot(q.T, D), q)
part_4 = epsi * tao * v @ v.T
DD = D + part_2 - part_3 + part_4
xxx = xx - alpha * np.dot(DD, delta_xx)
red = np.linalg.norm(xxx)**2 + (alpha / 2) * np.linalg.norm(A @ xxx -
b)**2
if k % log_int == 0:
obj.append(red)
print('The %dth iteration, target value is %f' % (k, red))
e = np.linalg.norm(xxx - xx)
if e < error:
break
else:
x = np.copy(xx)
xx = np.copy(xxx)
D = np.copy(DD)
if show_x:
print('The current x is: ', x)
k += 1
print("Final x: ", xx)
print("Total steps: ", k)
if show_graph:
draw(obj, log_int)
return xx, k, obj
def ADMM(A, b, alpha=0.1, beta=0.01, show_x=True, show_graph=True, log_int=1):
n = A.shape[1]
x = np.random.rand(n, 1)
z = np.random.rand(n, 1)
landa = np.random.rand(n, 1)
k = 0
if show_x:
print("x starts with: ")
print(x)
red = np.linalg.norm(x, ord=1) + (alpha / 2) * np.linalg.norm(A @ x - b)**2
print('The initial target value is %f' % (red))
obj = []
I = np.identity(n)
zero = np.zeros(n)
zero = zero.T
while (1):
#print(I)
#此处的landa是向量
temp1 = np.linalg.inv(alpha * (A.T @ A) + beta * I)
#print(temp1)
temp2 = alpha * (A.T @ b) + beta * z - landa
xx = temp1 @ temp2
#print(xx)
zz = np.copy(z)
zz = np.sign(xx + landa / beta) * np.maximum(
np.abs(xx + landa / beta) - 1 / beta, 0)
landalanda = landa + beta * (xx - zz)
red = np.linalg.norm(
xx, ord=1) + (alpha / 2) * np.linalg.norm(A @ xx - b)**2
if k % log_int == 0:
obj.append(red)
if k % log_int == 0:
print('The %dth iteration, target value is %f' % (k, red))
'''
xzk = np.vstack((x, z))
xzkp = np.vstack((xx, zz))
e = np.linalg.norm(xzk - xzkp)
if e <= error:
break
'''
if stop(I, xx, -I, zz, z, zero, landalanda, alpha):
break
else:
x = np.copy(xx)
z = np.copy(zz)
landa = np.copy(landalanda)
if show_x:
print('The current x is: ', x)
k += 1
print("Final x: ", xx)
print("Total steps: ", k)
if show_graph:
draw(obj, log_int)
return xx, k, obj
def ADMM(A,
b,
alpha=0.1,
beta=0.01,
show_x=True,
show_graph=True,
log_int=1,
max_step=-1):
#ADMM(x, alpha, landa, A, b, beta, z, D):
n = A.shape[1]
x = np.random.rand(n, 1)
z = np.random.rand(n, 1)
landa = np.random.rand(n, 1)
k = 0
if show_x:
print("x starts with: ")
print(x)
red = np.linalg.norm(x, ord=1) + (alpha / 2) * np.linalg.norm(A @ x - b)**2
print('The initial target value is %f' % (red))
obj = []
I = np.identity(n)
one = np.ones((n, 1))
zero = np.zeros((n, 1))
zeros = np.zeros((n, n))
D = np.eye(n)
D *= beta
while (1):
temp1 = np.linalg.inv(alpha * (A.T @ A) + D)
temp2 = alpha * (A.T @ b) + (D @ z) - landa
xx = temp1 @ temp2
temp1 = np.linalg.inv(2 * I + D)
temp2 = landa + D @ xx
zz = temp1 @ temp2
landalanda = landa + D @ (xx - zz)
red = np.linalg.norm(
xx, ord=1) + (alpha / 2) * np.linalg.norm(A @ xx - b)**2
if k % log_int == 0:
obj.append(red)
print('The %dth iteration, target value is %f' % (k, red))
if k == max_step:
break
if stop(I, xx, -I, zz, z, zero, landalanda, alpha):
break
else:
r = xx - zz
s = -1 * alpha * (zz - z)
u = 10
t_incr = 2
t_decr = t_incr
tmp = np.abs(r) - u * np.abs(s)
tmp = np.where(tmp > 0, t_incr, 1)
D *= tmp
tmp = np.abs(s) - u * np.abs(r)
tmp = np.where(tmp > 0, 1 / t_decr, 1)
D *= tmp
x = np.copy(xx)
z = np.copy(zz)
landa = np.copy(landalanda)
if show_x:
print('The current x is: ', x)
k += 1
print("Final x: ", xx)
print("Total steps: ", k)
if show_graph:
draw(obj, log_int)
return xx, k, obj