def r(f, h: LinearRestrictions):
"""
r(x, ν) = (∇f(x) + A.T ν, Ax − b)
"""
return lambda x, ν: concatenate([[
ConstrainedNewtonInfeasible.r_primal(f, h, x, ν)
], [ConstrainedNewtonInfeasible.r_dual(h, x)]])
def b(self):
x = self.x
f = self.f
A = self.h.A
b = self.h.b
ν = self.ν
return -concatenate([[f.gradient(x) + A.T @ ν], [A @ x - b]])
def b(self):
x = self.x
f = self.f
A = self.h.A
zeros_shape = A.shape[0]
zeros = np.zeros((zeros_shape, 1))
return -concatenate([[f.gradient(x)], [zeros]])
def A(self):
A = self.h.A
H = self.f.hessian(self.x)
zeros_shape = A.shape[0]
zeros = np.zeros((zeros_shape, zeros_shape))
return concatenate([
[H, A.T],
[A, zeros],
])
def kkt_elimination(A, b, matrix):
"""
:param A: A da matriz KKT
:param b: b da matriz KKT
:param matrix: matriz Kkt
:return:
"""
x = matrix.x
A = matrix.h.A # A matriz 'A' utilizada é a matriz de restrições
H = matrix.f.hessian(x)
H_inv = np.linalg.inv(H)
# Extract 'g' and 'h' from -b
g, h = np.split(-b, [x.shape[0]])
w = np.linalg.solve(A @ H_inv @ A.T, h - A @ H_inv @ g)
v = np.linalg.solve(H, -(g + A.T @ w))
return concatenate([[v], [w]])