python实现二次罚函数法目标函数为： -x1*x2约束条件分别为：-x1-x2^2+1=<0,x1+x2>=0

实现二次罚函数法可以分为以下几个步骤：

1. 定义目标函数和约束条件函数

def objective(x):
    return -x[0]*x[1]

def constraint1(x):
    return -x[0] - x[1]**2 + 1

def constraint2(x):
    return x[0] + x[1]

2. 定义二次罚函数

def penalty_func(x, penalty_coef):
    return objective(x) + penalty_coef*(max(0, constraint1(x))**2 + max(0, constraint2(x))**2)

3. 实现二次罚函数法优化算法

def quadratic_penalty_method(x0, penalty_coef, max_iter=1000, tol=1e-6):
    x = x0
    iter_count = 0
    while iter_count < max_iter:
        # 定义目标函数
        func = lambda x: penalty_func(x, penalty_coef)

        # 求解优化问题
        res = minimize(func, x, method='BFGS')

        # 判断是否满足收敛条件
        if abs(func(x) - func(res.x)) < tol:
            return res.x, func(res.x)

        # 更新参数
        x = res.x
        penalty_coef *= 2
        iter_count += 1

    return x, func(x)

4. 进行测试

x0 = [0, 0]
penalty_coef = 1
res = quadratic_penalty_method(x0, penalty_coef)
print(res)

完整代码如下：

from scipy.optimize import minimize

def objective(x):
    return -x[0]*x[1]

def constraint1(x):
    return -x[0] - x[1]**2 + 1

def constraint2(x):
    return x[0] + x[1]

def penalty_func(x, penalty_coef):
    return objective(x) + penalty_coef*(max(0, constraint1(x))**2 + max(0, constraint2(x))**2)

def quadratic_penalty_method(x0, penalty_coef, max_iter=1000, tol=1e-6):
    x = x0
    iter_count = 0
    while iter_count < max_iter:
        # 定义目标函数
        func = lambda x: penalty_func(x, penalty_coef)

        # 求解优化问题
        res = minimize(func, x, method='BFGS')

        # 判断是否满足收敛条件
        if abs(func(x) - func(res.x)) < tol:
            return res.x, func(res.x)

        # 更新参数
        x = res.x
        penalty_coef *= 2
        iter_count += 1

    return x, func(x)

x0 = [0, 0]
penalty_coef = 1
res = quadratic_penalty_method(x0, penalty_coef)
print(res)