def optimize(self):
# assert self.model
# Solve
self.model.optimize()
n = len(self.getX())
x = np.zeros((n, 1))
if self.model.status == GRB.status.OPTIMAL:
for i in xrange(n):
x[i][0] = self.getX()[i].x
# f(x) + 1/2 * rho * ||x - K||2
f_opt = self.model.ObjVal
prox = x - self.K
prox = dnrm2(prox)
prox *= self.rho
prox *= 0.5
# f(x)
f_opt -= prox
return (x, f_opt)
def optimizeX(self):
# assert self.model
# Solve
self.model_x.optimize()
x = np.zeros((self.n, 1))
if self.model_x.status == GRB.status.OPTIMAL:
for i in xrange(self.n):
x[i][0] = self.getX()[i].x
# f(x) + 1/2 * rho * ||A * x + B * zk - c + uk||2
f_opt = self.model_x.ObjVal
prox = self.prox_x # B * zk - c + uk
if(self.A is not None):
prox += np.dot(self.A, x)
prox = dnrm2(prox) # ||A * x + B * zk - c + uk||2
prox *= self.rho
prox *= 0.5
# f(x)
f_opt -= prox
return (x, f_opt)
def _unitvec_l2(self, vec):
return dscal(1.0 / dnrm2(vec), vec)
####
##
## ADMM convergence criteria
##
## x ∈ Rn and z ∈ Rm, where A ∈ Rp×n, B ∈ Rp×m, and c ∈ Rp
##
## For exchange A = 1 and B = -1
##
## e_pri = sqrt(p)+ e_abs + e_rel * max{Axk2,Bzk2,c2},
## e_dual = sqrt(n) + e_abs + e_rel * A.T x yk2
##
## This time n = p = T
#######
# rk+1 = Axk+1 + Bzk+1 − c
r_norm = np.sqrt(N) * dnrm2(x_mean)# r_i = x_mean => sqrt(sum ||r_i||_2^2) = sqrt(N * ||x_mean||_2^2)
# |ρ * A.TxB * (zk+1 − zk)|2
s_norm = rho * nzdiffstack # |ρ * -1 * (zk+1 − zk)|2 = ρ * |zk+1 − zk|2
# as described above
eps_pri = np.sqrt(T) * ABSTOL + RELTOL * max(nxstack, nzstack)
eps_dual = np.sqrt(T) * ABSTOL + RELTOL * nystack
# current snapshot
if(rank == 0 and DISP):
print ("\n%3d\t%10.3f\t%10.3f\t%10.3f\t%10.3f\t%10.3f\t%10.3f" %
(k, rho, r_norm, eps_pri, s_norm, eps_dual,cost))
# save history
if (rank == 0):
