python - 当你想计算梯度和目标函数时，如何使用 scipy.optimize.minimize 函数？

Question

scipy.optimize.minimze 将 obj 和 jac 函数作为输入。我相信它会在需要时分别调用它们。但我们经常会遇到目标函数，其梯度计算与目标函数共享大量计算。所以理想情况下，我想同时计算 obj 和 grad 。但是这个库好像不是这样的？如果有scipy.optimize.minimze如果有的话，有什么办法处理？

Answer 1

你完全可以。只需使用 jac=True:

In [1]: import numpy as np

In [2]: from scipy.optimize import minimize

In [3]: def f_and_grad(x):
   ...:     return x**2, 2*x
   ...: 

In [4]: minimize(f_and_grad, [1], jac=True)
Out[4]: 
      fun: 1.8367099231598242e-40
 hess_inv: array([[ 0.5]])
      jac: array([  2.71050543e-20])
  message: 'Optimization terminated successfully.'
     nfev: 4
      nit: 2
     njev: 4
   status: 0
  success: True
        x: array([  1.35525272e-20])

实际上是documented :

jac : bool or callable, optional Jacobian (gradient) of objective function. Only for CG, BFGS, Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg. If jac is a Boolean and is True, fun is assumed to return the gradient along with the objective function. If False, the gradient will be estimated numerically. jac can also be a callable returning the gradient of the objective. In this case, it must accept the same arguments as fun.

(强调我的)