import matplotlib.pyplot as plt
import numpy as np
import cvxpy as cp

x=cp.Variable(6,pos=True)
obj=cp.Minimize(x[5])
a1=np.array([0.025, 0.015, 0.055, 0.026])
a2=np.array([0.05, 0.27, 0.19, 0.185, 0.185])
a3=np.array([1, 1.01, 1.02, 1.045, 1.065])
k=0.05; kk=[]; qq=[]
while k<0.27:
con=[cp.multiply(a1,x[1:5])-x[5]<=0,a2@x[:-1]>=k, a3@x[:-1]==1]
prob=cp.Problem(obj,con)
prob.solve(solver='GLPK_MI')
kk.append(k); qq.append(prob.value)
k=k+0.005
prob.solve(solver='ECOS')
plt.rc('text',usetex=False); plt.rc('font',size=16); plt.rc('font',family='SimHei')
plt.plot(kk,qq,'k')
plt.plot(kk,qq,'b.')
plt.xlabel("收益 k"); plt.ylabel("风险 Q",rotation=0)
plt.show()

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