def BusquedaLineal_amplio(f, x0, metodo="maximo descenso"):
xk=x0
if metodo == "Newton":
while not (f_o_c(f,xk)) and (s_o_c(f,xk)):
grad=Grad(f, xk)
hess=Hess(f,xk)
pk=LA.solve(hess,-grad)
alpha = genera_alpha(f,x0,pk)
xk= xk + alpha*pk
else:
while not (f_o_c(f,xk)) and (s_o_c(f,xk)):
grad=Grad(f,xk)
pk = -grad
alpha = genera_alpha(f,xk,pk)
xk = xk + alpha*pk
return xk
def NewMod(f,xk,h,maxIt=100):
Bk = Hess(f,xk,h)
for k in range(maxIt):
while not is_pos_def(Bk):
Bk=modificacion_hessiana(Bk)
pk = LA.inv(Bk).dot(-Grad(f,xk))
a = genera_alpha(1,f,xk,pk,h)
xk = xk + a*pk
return xk
def busqueda_lineal(f, x0, method='Maximo Descenso'):
xk = x0
while not (is_min(f, xk)):
grad = Grad(f, xk)
hess = Hess(f, xk)
if method == 'Newton':
hess = modificacion_hessiana(hess)
pk = np.linalg.solve(hess, -grad)
elif method == 'Maximo Descenso':
pk = -grad
alpha = genera_alpha(f, xk, pk)
xk = xk + alpha * pk
return xk
def BFGS(f, x0, tol, H0, maxiter=10000):
k = 0
Gk = Grad(f, x0)
Hk = H0
xk = np.array(x0)
xk1 = np.array(x0)
sk = np.array(100)
while (LA.norm(Gk) > tol and LA.norm(sk) > tol and k <= maxiter):
pk = -Hk.dot(Gk)
alphak = genera_alpha(f, xk, pk)
xk1 = xk + alphak * pk
sk = xk1 - xk
Gk1 = Grad(f, xk1)
yk = Gk1 - Gk
Hk = DFP_Hk(yk, sk, Hk)
k += 1
xk = xk1
Gk = Gk1
return xk1, k