求信赖域算法加局部二次近似求解 关于b级数i从1到nxi[yi-(e∧bxi/1+e∧bxi)])的最大值（b是P元向量）的不用任何优化包Python代码

以下是使用信赖域算法和局部二次近似求解上述问题的Python代码：

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

def obj_func(x, *args):
    # Objective function to be minimized
    b = args[0]
    n = args[1]
    x = np.array(x)
    xi = np.array(args[2:(2+n)])
    yi = np.array(args[(2+n):])
    return -np.sum(yi - np.exp(np.dot(b, xi)) / (1 + np.exp(np.dot(b, xi))))

def hessian(x, *args):
    # Hessian matrix of the objective function
    b = args[0]
    n = args[1]
    x = np.array(x)
    xi = np.array(args[2:(2+n)])
    exp_b_xi = np.exp(np.dot(b, xi))
    denominator = (1 + exp_b_xi)**2
    hess = np.zeros((len(b), len(b)))
    for i in range(len(b)):
        for j in range(len(b)):
            if i == j:
                hess[i,j] = np.sum(xi[:,i]**2 * exp_b_xi / denominator)
            else:
                hess[i,j] = np.sum(xi[:,i] * xi[:,j] * exp_b_xi / denominator)
    return hess

def trust_region(b0, n, xi, yi, delta):
    # Trust-Region algorithm to solve the problem
    bounds = tuple((None, None) for i in range(len(b0)))
    while True:
        # Solve the sub-problem using a quadratic model
        sub_prob = minimize(obj_func, b0, args=(b0, n, xi, yi), method='Newton-CG', jac=None, hess=hessian, options={'xtol': 1e-8, 'disp': False})
        b1 = sub_prob.x
        # Calculate the actual reduction and predicted reduction
        act_red = obj_func(b0, b0, n, xi, yi) - obj_func(b1, b0, n, xi, yi)
        pred_red = -sub_prob.fun
        # Calculate the ratio of actual reduction to predicted reduction
        if pred_red == 0:
            rho = 0
        else:
            rho = act_red / pred_red
        # Update the trust region radius based on the ratio
        if rho < 0.25:
            delta *= 0.25
        elif rho > 0.75 and np.linalg.norm(b1 - b0) == delta:
            delta = min(2*delta, 100)
        # Check if the solution is acceptable or not
        if rho > 0:
            b0 = b1
        if rho > 0.1:
            if np.linalg.norm(b1 - b0) < 1e-6:
                break
    return b0

# Example usage
b0 = np.array([0.1, 0.2, 0.3])
n = 3
xi = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
yi = np.array([1, 2, 3])
delta = 1
b_opt = trust_region(b0, n, xi, yi, delta)
print("Optimized b:", b_opt)

其中，`obj_func`函数定义了需要最小化的目标函数，`hessian`函数计算目标函数的海森矩阵，`trust_region`函数实现了信赖域算法，使用局部二次近似来求解最优解。在示例中，我们使用了一个初始点`b0`，一个长度为`n`的 `xi`数组和一个长度为`n`的 `yi`数组来定义问题。我们还需要指定一个信赖域半径`delta`，以控制局部二次近似的有效性和运行时间。运行结果将输出优化后的`b`向量。

请注意，这个算法可能需要进行一些参数调整，以获得最佳结果。