def vmax_continuous(self, Value, s, xij, i, j):
xl, xu = self.bounds(s, i, j)
for it in range(self.options.maxitncp):
vv, vx, vxx = self.__Bellman_rhs(Value, s, xij, i, j)
# Compute Newton step, update continuous action, check convergence
vx, delx = lcpstep(self.options.ncpmethod, xij, xl, xu, vx, vxx)
xij[:] += delx
if np.linalg.norm(vx.flatten(), np.Inf) < self.options.tol:
break
return self.__Bellman_rhs(Value, s, xij, i, j)[0][0]
def vmax_continuous_restricted(self, Value, s, xij, i, j):
ns = s.shape[-1]
dx = self.dims.dx
xl, xu = self.bounds(s, i, j)
dr = self.restrictions(s, xij, i, j).shape[0]
lij = np.ones((dr, ns))
xl = np.vstack((xl, np.zeros((dr, ns))))
xu = np.vstack((xu, np.tile(np.inf, (dr, ns))))
ZEROS = np.zeros((dr, dr, ns))
for it in range(self.options.maxitncp):
vv, vx, vxx = self.__Bellman_rhs(Value, s, xij, i, j)
# Adjust derivative to add the Lagrange multiplier term
h, hx, hxx = self.restrictions(s, xij, i, j, True)
for ir in range(dr):
vx += lij[ir] * hx[ir]
vxx += lij[ir] * hxx[ir]
vx = np.vstack((vx, -h))
vxx = np.vstack((np.hstack((vxx, np.swapaxes(hx, 0,1))),
np.hstack((-hx, ZEROS))))
# Compute Newton step, update continuous action, check convergence
vx, delxl = lcpstep(self.options.ncpmethod,
np.vstack((xij, lij)),
xl, xu, vx, vxx)
delx, dell = np.split(delxl, [dx])
xij[:] += delx
lij[:] += dell
print('it = ', it, '\tchange = ', np.linalg.norm(vx.flatten(), np.Inf))
if np.linalg.norm(vx.flatten(), np.Inf) < self.options.tol:
break
return self.__Bellman_rhs(Value, s, xij, i, j)[0][0]