scipy 的最小化功能是否使用方法“COBYLA"?接受界限? [英] Does scipy's minimize function with method "COBYLA" accept bounds?

问题描述

我在 scipy 的 optimize.minimize 函数(针对 cygwin 的 v.0.11 版本)中使用算法 'COBYLA'.我观察到在这种情况下似乎没有使用参数 bounds.举个简单的例子:

I'm using the algorithm 'COBYLA' in scipy's optimize.minimize function (v.0.11 build for cygwin). I observed that the parameter bounds seems not to be used in this case. For instance, the simple example:

from scipy.optimize import minimize

def f(x):
    return -sum(x)

minimize(f, x0=1, method='COBYLA', bounds=(-2,2))

返回:

status: 2.0
nfev: 1000
maxcv: 0.0
success: False
fun: -1000.0
x: array(1000.0)
message: 'Maximum number of function evaluations has been exceeded.'

而不是 x 的预期 2.

有没有人发现同样的问题?是否存在已知错误或文档错误?在 scipy 0.11 文档中，COBYLA 算法不排除此选项.事实上，函数 fmin_cobyla 没有 bounds 参数.感谢您的任何提示.

Did anyone perceived the same problem? Is there a known bug or documentation error? In the scipy 0.11 documentation, this option is not excluded for the COBYLA algorithm. In fact the function fmin_cobyla doesn't have the bounds parameter. Thanks for any hint.

推荐答案

你可以用约束的形式来制定边界

You can formulate the bounds in the form of constraints

import scipy
#function to minimize
def f(x):
    return -sum(x)
#initial values
initial_point=[1.,1.,1.]    
#lower and upper bound for variables
bounds=[ [-2,2],[-1,1],[-3,3]   ]

#construct the bounds in the form of constraints
cons = []
for factor in range(len(bounds)):
    lower, upper = bounds[factor]
    l = {'type': 'ineq',
         'fun': lambda x, lb=lower, i=factor: x[i] - lb}
    u = {'type': 'ineq',
         'fun': lambda x, ub=upper, i=factor: ub - x[i]}
    cons.append(l)
    cons.append(u)

#similarly aditional constrains can be added

#run optimization
res = scipy.optimize.minimize(f,initial_point,constraints=cons,method='COBYLA')
#print result
print res

请注意，最小化函数将为函数提供设计变量.在这种情况下，3 个输入变量有 3 个上限和下限.结果产生:

Note that the minimize function will give the design variables to the function. In this case 3 input variables are given with 3 upper and lower bounds. the result yields:

   fun: -6.0
   maxcv: -0.0
 message: 'Optimization terminated successfully.'
    nfev: 21
  status: 1
 success: True
       x: array([ 2.,  1.,  3.])

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