Matlab和Python中的优化算法(狗腿信任区域) [英] Optimization algorithm (dog-leg trust-region) in Matlab and Python

问题描述

我正在尝试使用Matlab和Python中的狗腿信任区域算法来求解一组非线性方程.

I'm trying to solve a set of nonlinear equations using the dog-leg trust-region algorithm in Matlab and Python.

在Matlab中，有 fsolve ，该算法是默认算法，而对于Python，我们在

In Matlab there is fsolve where this algorithm is the default, whereas for Python we specify 'dogleg' in scipy.optimize.minimize. I won't need to specify a Jacobian or Hessian for the Matlab whereas Python needs either one to solve the problem.

我没有Jacobian/Hessian，所以对于Python，有没有办法解决这个问题?还是在fsolve中有另一个函数执行与Matlab的dog-leg方法等效的功能?

I don't have the Jacobian/Hessian so is there a way around this issue for Python? Or is there another function that performs the equivalent of Matlab's dog-leg method in fsolve?

推荐答案

在较新版本的scipy中，有

In newer versions of scipy there is the approx_fprime function. It computes a numerical approximation of the jacobian of function f at position xk using the foward step finite difference. It returns an ndarray with the partial derivate of f at positions xk.

如果无法升级scipy版本，则始终可以从

If you can't upgrade your version of scipy, you can always copy the implementation from scipy's source.

scipy.optimize.minimize在内部调用approx_fprime.因此，在您的情况下，只需执行以下操作即可:

scipy.optimize.minimize calls approx_fprime internally if the input jac=False. So in your case, it should be enough to do the following:

scipy.optimize.minimize(fun, x0, args, method='dogleg', jac=False)

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编辑

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Edit

scipy似乎无法正确处理jac=False条件，因此有必要使用approx_fprime如下构建可调用的jac

scipy does not seem to handle the jac=False condition properly so it is necessary to build a callable jac using approx_fprime as follows

jac = lambda x,*args: scipy.optimize.approx_fprime(x,fun,epsilon,*args)
scipy.optimize.minimize(fun, x0, args, method='dogleg', jac=jac)

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