Python 如何在有约束的 scipy 中使用最小化函数
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How do I use a minimization function in scipy with constraints
提问by anand
I need some help regarding optimisation functions in python(scipy)
the problem is optimizing f(x)where x=[a,b,c...n]. the constraints are that values of a,b etc should be between 0 and 1, and sum(x)==1. The scipy.optimise.minimize function seems best as it requires no differential. How do I pass the arguments?
我需要一些有关 python(scipy) 中优化函数的帮助，问题是优化f(x)where x=[a,b,c...n]。约束是 a、b 等的值应介于 0 和 1 之间，并且sum(x)==1. scipy.optimise.minimize 函数似乎最好，因为它不需要差分。我如何传递参数？
Creating an ndarray using permutation is too long. My present code as below:-
使用排列创建 ndarray 太长了。我现在的代码如下：-
import itertools as iter
all=iter.permutations([0.0,.1,.2,.3,.4,.5,.6,.7,.8,.9,1.0],6) if sum==1
all_legal=[]
for i in all:
if np.sum(i)==1:
#print np.sum(i)
all_legal.append(i)
print len(all_legal)
lmax=0
sharpeMax=0
for i in all_legal:
if sharpeMax<getSharpe(i):
sharpeMax=getSharpe(i)
lmax=i
回答by CT Zhu
Check .minimizedocstring:
检查.minimize文档字符串：
scipy.optimize.minimize(fun, x0, args=(), method='BFGS', jac=None, hess=None, hessp=None, \
bounds=None, constraints=(), tol=None, callback=None, options=None)
What matters the most in your case will be the bounds. When you want to constrain your parameter in [0,1] (or (0,1)?) You need to define it for each variable, such as:
在您的情况下最重要的是bounds. 当你想将你的参数限制在 [0,1]（或（0,1）？）中时，你需要为每个变量定义它，例如：
bounds=((0,1), (0,1).....)
Now, the other part, sum(x)==1. There may be more elegant ways to do it, but consider this: instead of minimizing f(x), you minimize h=lambda x: f(x)+g(x), a new function essential f(x)+g(x)where g(x)is a function reaches it minimum when sum(x)=1. Such as g=lambda x: (sum(x)-1)**2.
现在，另一部分，sum(x)==1。可能有更优雅的方法来做到这一点，但请考虑这一点：不是最小化f(x)，而是最小化h=lambda x: f(x)+g(x)，这是一个必不可少的新函数f(x)+g(x)，其中g(x)函数在 时达到最小值sum(x)=1。比如g=lambda x: (sum(x)-1)**2。
The minimum of h(x)is reached when both f(x)and g(x)are at their minimum. Sort of a case of Lagrange multiplier method http://en.wikipedia.org/wiki/Lagrange_multiplier
最小h(x)达到当两个f(x)和g(x)处于最小。拉格朗日乘数法的一个例子http://en.wikipedia.org/wiki/Lagrange_multiplier
回答by Daniel
You can do a constrained optimization with COBYLAor SLSQPas it says in the docs.
您可以使用COBYLA或SLSQP按照文档中的说明进行约束优化。
from scipy.optimize import minimize
start_pos = np.ones(6)*(1/6.) #or whatever
#Says one minus the sum of all variables must be zero
cons = ({'type': 'eq', 'fun': lambda x: 1 - sum(x)})
#Required to have non negative values
bnds = tuple((0,1) for x in start_pos)
Combine these into the minimization function.
将这些组合到最小化函数中。
res = minimize(getSharpe, start_pos, method='SLSQP', bounds=bnds ,constraints=cons)
