多元极小化的最小示例

Question

因此，我正在尝试用不止一个示例来编写一个最小的scipy.optimize.minimize工作示例。

基本上，我的示例适用于一个变量的lambda函数，但是一旦我添加了另一个变量，它就崩溃了。

lamX = lambda x: (x-2)**2
q0X = np.ones(1)
solX = optimize.minimize(lamX, x0=q0X)

lamXY = lambda x,y: (x-2)**2 + y**2
q0XY = np.ones(2)
solXY = optimize.minimize(lamXY, x0=q0XY)

前三行执行时没有出现错误，并给出了正确的结果，但后三行给出了以下错误

    solXY = optimize.minimize(lamXY, x0=q0XY)
  File "/usr/lib/python3/dist-packages/scipy/optimize/_minimize.py", line 444, in minimize
    return _minimize_bfgs(fun, x0, args, jac, callback, **options)
  File "/usr/lib/python3/dist-packages/scipy/optimize/optimize.py", line 913, in _minimize_bfgs
    gfk = myfprime(x0)
  File "/usr/lib/python3/dist-packages/scipy/optimize/optimize.py", line 292, in function_wrapper
    return function(*(wrapper_args + args))
  File "/usr/lib/python3/dist-packages/scipy/optimize/optimize.py", line 688, in approx_fprime
    return _approx_fprime_helper(xk, f, epsilon, args=args)
  File "/usr/lib/python3/dist-packages/scipy/optimize/optimize.py", line 622, in _approx_fprime_helper
    f0 = f(*((xk,) + args))
  File "/usr/lib/python3/dist-packages/scipy/optimize/optimize.py", line 292, in function_wrapper
    return function(*(wrapper_args + args))
TypeError: <lambda>() missing 1 required positional argument: 'y'

谁能给我一个提示，我哪里做错了？

Answer 1

您的lambda需要为x使用一个类似数组的对象。我用下面的代码让它工作起来：

>>> lamXY = lambda x: (x[0]-2)**2 + x[1]**2
>>> q0XY = np.ones(2)
>>> solXY = optimize.minimize(lamXY, x0=q0XY)
>>> solXY
      fun: 3.865407235741147e-16
 hess_inv: array([[0.75, 0.25],
       [0.25, 0.75]])
      jac: array([-9.04871520e-09, -1.62848344e-08])
  message: 'Optimization terminated successfully.'
     nfev: 12
      nit: 2
     njev: 3
   status: 0
  success: True
        x: array([ 1.99999999e+00, -1.55929978e-08])

虽然这通常不适用于python中的lambda，但看起来scipy希望lambda只有一个输入变量。