题

您可以像这样将问题 A 解决为二阶锥程序：

#!/usr/bin/env python3

import cvxpy as cp 
import numpy as np

##########################
#Question A
##########################

n = 50                          #Arbitrary number of dimensions
r = 10                          #Arbitrary radius
e = 3                           #Epsilon value
a = np.random.random(size=50)   #Generate random a vector
a = a/np.linalg.norm(a, ord=2)  #Scale to unit length
a = r*a                         #Scale to radius

x = cp.Variable(shape=n)        #x, a variable to be optimized
cons = []                       #List of constraints

#See cvxpy's atoms here: https://www.cvxpy.org/api_reference/cvxpy.atoms.html
cons += [cp.norm(x+a,2)<=r]     #Note that we are using cvxpy's `norm` function!
cons += [cp.norm_inf(x)<=e]

#Objective
obj = cp.Maximize(cp.sum(a*x))

#Formulate problem
prob = cp.Problem(obj, cons)

#Solve problem
optval = prob.solve()

print("Optimum value = {0}".format(optval))
print("x = {0}".format(x.value))

问题 B 您无法使用 cvxpy 即插即用解决问题，因为问题是非凸的（您正在对椭球表面进行优化）。