试图解决最大化函数

Question

我有一个要解决的最大化问题：

为此，我期待使用minimize库中的scipy函数。

在尝试之前，我将定义每个变量：

mu=[[-0.241035],
    [ 0.03557551],
    [-0.00410642],
    [-0.43985304],
    [-0.24741543]]

landa= 42.74650697 # is a scalar

E =[[0.000167,0.000032,0.000082,0.000055,0.000055],
[0.000032,0.000131,0.000019,0.000043,0.000032],
[0.000082,0.000019,0.000273,0.000110,0.000086],
[0.000055,0.000043,0.000110,0.000229,0.000131],
[0.000055,0.000032,0.000086,0.000131,0.000165]]

在funct0中，设置出现在图像中的“最大化”函数并定义权重矩阵。

def funct0(x):
    x0,x1,x2,x3,x4=x
    weights= np.array([x0,x1,x2,x3,x4])
    return -1*(np.matmul(weights.T , mu) - np.matmul(np.matmul (landa*weights.T, E ),weights) /2)

在funct1中设置边界和约束，因为我希望权重x0,x1,x2,x3,x4中的变量总和为1。

def funct1():
    x0=np.array([1,1,1,1,1])
    cons = ({'type': 'eq', 'fun': lambda x:  sum(x) - 1})
    res=minimize(funct0, x0, bounds=[[0,None] for i in range(len(x0))],options={"disp": False}, constraints=cons)
    return res.x

 print(funct1())

执行此脚本时，它输出

[  0   1   0   0  0]

我不确定最大化是否正确，因为它将全部分配给x1变量，而其余x0 x2 x3 x4被分配了0个值

如果在funct0中设置的函数是w和mu的线性函数，这对我来说很有意义，因为这样做会将所有值分配给对应的x1达到mu

中的最高值

考虑到函数的非线性，我想我的输出将是矩阵中w变量之间值的更“多样化”分配。

是否可能在funct0中错误地设置了功能？ 我可能使用了错误的优化吗？

我们非常感谢您的帮助。