在强劲的租赁方期间，CVXOPT产生nan

Question

我试图从cvxopt documentation中重现“鲁棒最小二乘”示例：

import numpy as np
import cvxopt

def robls(A, b, rho):
    m, n = A.size
    def F(x=None, z=None):
        if x is None: return 0, cvxopt.matrix(0.0, (n,1))
        y = A*x-b
        w = cvxopt.sqrt(rho + y**2)
        f = sum(w)
        Df = cvxopt.div(y, w).T * A
        assert not np.isnan(f)
        assert not np.isnan(np.array(Df)).any()
        if z is None: return f, Df
        H = A.T * cvxopt.spdiag(z[0]*rho*(w**-3)) * A
        assert not np.isnan(np.array(H)).any()
        return f, Df, H
    return cvxopt.solvers.cp(F)['x']

这个例子应该为x解min sqrt{ρ + (Ax - b)²}。如果矩阵A是恒等式，那么解显然是x=b。这也适用于

b = np.ones(2)
robls(cvxopt.matrix(np.eye(2)), cvxopt.matrix(b), 1e-2)

而且当我用b = 3 * np.ones(2)或b = 4 * np.ones(2)代替时

但是，对于b = 2 * np.ones(2)，我得到一个错误：

     pcost       dcost       gap    pres   dres
 0:  0.0000e+00  4.0050e+00  1e+00  1e+00  1e+00
 1: -1.5820e+03  1.5840e+03  1e-02  6e+02  1e+00
 2: -9.8358e+10  9.8358e+10  1e-04  4e+10  1e+00
 3: -2.3551e+34  2.3551e+34  1e-06  9e+33  1e+00
 4: -3.2329e+104  3.2329e+104  1e-08 1e+104  1e+00

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-17-5e542f22beda> in <module>
     16 
     17 b = 2 * np.ones(2)
---> 18 robls(cvxopt.matrix(np.eye(2)), cvxopt.matrix(b), 1e-2)

<ipython-input-17-5e542f22beda> in robls(A, b, rho)
     13         assert not np.isnan(np.array(H)).any()
     14         return f, Df, H
---> 15     return cvxopt.solvers.cp(F)['x']
     16 
     17 b = 2 * np.ones(2)

~/.anaconda3/envs/myenv2020/lib/python3.7/site-packages/cvxopt/cvxprog.py in cp(F, G, h, dims, A, b, kktsolver, xnewcopy, xdot, xaxpy, xscal, ynewcopy, ydot, yaxpy, yscal, **kwargs)
   1964 
   1965     sol = cpl(c, F_e, G_e, h, dims, A_e, b, kktsolver_e, xnewcopy_e, 
-> 1966          xdot_e, xaxpy_e, xscal_e, options = options)
   1967 
   1968     sol['x'] = sol['x'][0]

~/.anaconda3/envs/myenv2020/lib/python3.7/site-packages/cvxopt/cvxprog.py in cpl(c, F, G, h, dims, A, b, kktsolver, xnewcopy, xdot, xaxpy, xscal, ynewcopy, ydot, yaxpy, yscal, **kwargs)
   1054             while backtrack:
   1055                 xcopy(x, newx);  xaxpy(dx, newx, alpha = step)
-> 1056                 t = F(newx)
   1057                 if t is None: newf = None
   1058                 else: newf, newDf = t[0], t[1]

~/.anaconda3/envs/myenv2020/lib/python3.7/site-packages/cvxopt/cvxprog.py in F_e(x, z)
   1778         else:
   1779             if z is None:
-> 1780                 v = F(x[0])
   1781                 if v is None or v[0] is None: return None, None
   1782                 val = matrix(v[0], tc = 'd')

<ipython-input-7-b500673e8f31> in F(x, z)
      4         if x is None: return 0, cvxopt.matrix(0.0, (n,1))
      5         y = A*x-b
----> 6         w = cvxopt.sqrt(rho + y**2)
      7         f = sum(w)
      8         Df = cvxopt.div(y, w).T * A

ValueError: domain error

通过对代码进行调试，我看到向量x中填充了nan：

ipdb> p np.array(x)
array([[nan],
       [nan]])

为什么呢？还有，我如何修复它