Python-求解带约束的最优化问题

题目：
 

利用拉格朗日乘子法

#导入sympy包，用于求导，方程组求解等等
from sympy import * 
 
#设置变量
x1 = symbols("x1")
x2 = symbols("x2")
alpha = symbols("alpha")
beta = symbols("beta")
 
#构造拉格朗日等式
L = 10 - x1*x1 - x2*x2 + alpha * (x1*x1 - x2) + beta * (x1 + x2)
 
#求导，构造KKT条件
difyL_x1 = diff(L, x1)  #对变量x1求导
difyL_x2 = diff(L, x2)  #对变量x2求导
difyL_beta = diff(L, beta)  #对乘子beta求导
dualCpt = alpha * (x1 * x1 - x2)  #对偶互补条件
 
#求解KKT等式
aa = solve([difyL_x1, difyL_x2, difyL_beta, dualCpt], [x1, x2, alpha, beta])
 
#打印结果，还需验证alpha>=0和不等式约束<=0
for i in aa:
    if i[2] >= 0:
        if (i[0]**2 - i[1]) <= 0:
            print(i)

转载地址：https://blog.csdn.net/qq_33757398/article/details/82834888