A = np.array([[2,-1,0,0,0,0,0,0,0,0],
              [-1,2,-1,0,0,0,0,0,0,0],
              [0,-1,2,-1,0,0,0,0,0,0],
              [0,0,-1,2,-1,0,0,0,0,0],
              [0,0,0,-1,2,-1,0,0,0,0],
              [0,0,0,0,-1,2,-1,0,0,0],
              [0,0,0,0,0,-1,2,-1,0,0],
              [0,0,0,0,0,0,-1,2,-1,0],
              [0,0,0,0,0,0,0,-1,2,-1],
              [0,0,0,0,0,0,0,0,-1,2]])


B = np.array([[1,0,0,0,0,0,0,0,0,0],
              [1,1,0,0,0,0,0,0,0,0],
              [1,1,1,0,0,0,0,0,0,0],
              [1,1,1,1,0,0,0,0,0,0],
              [1,1,1,1,1,0,0,0,0,0],
              [1,1,1,1,1,1,0,0,0,0],
              [1,1,1,1,1,1,1,0,0,0],
              [1,1,1,1,1,1,1,1,0,0],
              [1,1,1,1,1,1,1,1,1,0],
              [1,1,1,1,1,1,1,1,1,1]])

q = np.array([1,1,1,1,1,1,1,1,1,1]).reshape((10,1))
d = np.array([1,2,3,4,5,6,7,8,9,10]).reshape((10,1))

def count_x(lam):
    #x = A^-1(q-(lam^T*B)^T)/2
    x = np.linalg.inv(A)
    x = x.dot(q - np.dot(B.T, lam))
    return x / 2

def count_lam(x, lam, r):
    #lami = lami + r(fi(x))
    lam = lam + r * (np.dot(B, x) - d)
    lam = np.maximum(np.array([0,0,0,0,0,0,0,0,0,0]).reshape((10,1)), lam)
    return lam

def Problem(r=1, eps=0.01):
    x = np.array([0,0,0,0,0,0,0,0,0,0]).reshape((10,1))
    lam = np.array([1,1,1,1,1,1,1,1,1,1]).reshape((10,1))
    lam = count_lam(x, lam, r)
    x_new = count_x(lam)
    #print (x_new)
    #print(x)
    #print(np.linalg.norm(x - x_new))
    while (np.linalg.norm(x - x_new) > eps):
        x = x_new
        lam = count_lam(x, lam, r)
        x_new = count_x(lam)
    return x

Problem(r=0.0001, eps=0.0000001)