使用LinearConstraint调用scipy minimize报错：对象不可迭代

问题场景 #

尝试基于相关矩阵，使用LinearConstraint配合minimize执行最小化操作时，出现'LinearConstraint' object is not iterable或'LinearConstraint' object is not subscriptable错误。

所用相关矩阵（DataFrame格式）：

col1  col2  col3
1    1.00  0.59  0.68
2    0.59  1.00  0.92
3    0.68  0.92  1.00

执行代码：

from scipy.optimize import minimize, LinearConstraint
import numpy as np

A0 = [.3,.4,.3]
bnds = [(1, 1) for i in range(len(A0))]

def test(w):   
    return (w@np.matrix(corr))@w

temp=minimize(test,A0,constraints=(LinearConstraint(np.array([1,1,1]),lb=1.0,ub=1.0), ))

运行后报错：

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
C:\Program Files\Anaconda3\lib\site-packages\scipy\optimize\slsqp.py in _minimize_slsqp(func, x0, args, jac, bounds, constraints, maxiter, ftol, iprint, disp, eps, callback, **unknown_options)
    253         try:
--> 254             ctype = con['type'].lower()
    255         except KeyError:

TypeError: 'LinearConstraint' object is not subscriptable

During handling of the above exception, another exception occurred:

TypeError                                 Traceback (most recent call last)
<ipython-input-331-ce6c477d5282> in <module>
      8     return (w@np.matrix(corr))@w
      9 
---> 10 temp=minimize(test,A0,constraints=(LinearConstraint(np.array([1,1,1]),lb=1.0,ub=1.0), ))

C:\Program Files\Anaconda3\lib\site-packages\scipy\optimize\_minimize.py in minimize(fun, x0, args, method, jac, hess, hessp, bounds, constraints, tol, callback, options)
    609     elif meth == 'slsqp':
    610         return _minimize_slsqp(fun, x0, args, jac, bounds,
--> 611                                constraints, callback=callback, **options)
    612     elif meth == 'trust-constr':
    613         return _minimize_trustregion_constr(fun, x0, args, jac, hess, hessp,

C:\Program Files\Anaconda3\lib\site-packages\scipy\optimize\slsqp.py in _minimize_slsqp(func, x0, args, jac, bounds, constraints, maxiter, ftol, iprint, disp, eps, callback, **unknown_options)
    256             raise KeyError('Constraint %d has no type defined.' % ic)
    257         except TypeError:
--> 258             raise TypeError('Constraints must be defined using a '
    259                             'dictionary.')
    260         except AttributeError:

TypeError: Constraints must be defined using a dictionary.

错误原因 #

scipy.optimize.minimize的默认优化方法是SLSQP，该方法不支持直接传入LinearConstraint对象，要求约束必须以字典形式定义；而LinearConstraint是专为trust-constr优化方法设计的约束类型。

解决方法 #

方法1：使用trust-constr方法 #

在minimize调用中指定method='trust-constr'参数，即可直接使用LinearConstraint对象：

from scipy.optimize import minimize, LinearConstraint
import numpy as np

A0 = [.3,.4,.3]
bnds = [(1, 1) for i in range(len(A0))]

def test(w):   
    return (w@np.matrix(corr))@w

# 指定method为trust-constr
temp=minimize(test,A0,constraints=(LinearConstraint(np.array([1,1,1]),lb=1.0,ub=1.0), ), method='trust-constr')

方法2：改用字典形式定义约束（适配默认SLSQP方法） #

如果希望继续使用默认的SLSQP优化器，将约束转换为字典格式，指定type、fun等字段：

from scipy.optimize import minimize
import numpy as np

A0 = [.3,.4,.3]
bnds = [(1, 1) for i in range(len(A0))]

def test(w):   
    return (w@np.matrix(corr))@w

# 用字典定义线性约束：sum(w) = 1
constraint = {
    'type': 'eq',
    'fun': lambda w: np.sum(w) - 1
}

temp=minimize(test,A0,constraints=(constraint, ))

内容的提问来源于stack exchange，提问作者Sanchit Aluna