1

我正在尝试解决 cvxopt 中的二次问题，但似乎忽略了其中一项要求

我想解决这组方程：

    G =
    [-1.00e+00 -0.00e+00 -0.00e+00 -0.00e+00]
    [-0.00e+00 -1.00e+00 -0.00e+00 -0.00e+00]
    [-0.00e+00 -0.00e+00 -1.00e+00 -0.00e+00]
    [-0.00e+00 -0.00e+00 -0.00e+00 -1.00e+00]
    [ 1.00e+00  0.00e+00  0.00e+00  0.00e+00]
    [ 0.00e+00  1.00e+00  0.00e+00  0.00e+00]
    [ 0.00e+00  0.00e+00  1.00e+00  0.00e+00]
    [ 0.00e+00  0.00e+00  0.00e+00  1.00e+00]

    h = 
    [ 0.00]
    [ 0.00]
    [ 0.00]
    [ 0.00]
    [ 20.0]
    [ 20.0]
    [ 20.0]
    [ 20.0]

G <= h

这是代码：

import numpy as np
import pandas as pd
import cvxopt as opt
from cvxopt import solvers
from pandas.io.data import DataReader
from pandas.io.data import DataFrame

def get_returns(stock_list, start_date, end_date, shift = 100):
    raw_data = {}

    for ticker in stock_list:
        raw_data[ticker] = DataReader(ticker, 'yahoo', start_date, end_date)['Adj Close']

    price = DataFrame({ tic: data for tic, 
                                            data in raw_data.iteritems()})  

    returns = price/price.shift(shift) - 1
    returns = np.asmatrix(returns[shift:][:])

    return returns.T

def print_portfolio(stock_list, portfolio):
    for stock, weight in zip(stock_list, portfolio):
        print('\t %s \t: %.4f.' % (stock,weight))

    return

stock_list = ['AAPL','IBM','MSFT','ORCL']
start_date = '1/1/2011'     # start of the historical data  
end_date     = '1/1/2012'       # end of historical data

solvers.options['show_progress'] = False

returns = np.asmatrix(get_returns(stock_list, start_date, end_date))
n = len(returns)

N = 100
mus = [10**(5.0 * t/N - 1.0) for t in range(N)]

S = opt.matrix(np.cov(returns))
pbar = opt.matrix(np.mean(returns, axis=1))

G = -opt.matrix(np.eye(n))
G = opt.matrix(np.concatenate((G, -G), axis = 0))
print G

h = opt.matrix(np.concatenate((opt.matrix(0.0, (n ,1)), opt.matrix(0.20, (n ,1))), axis = 0))
print h

A = opt.matrix(1.0, (1, n))     #
b = opt.matrix(1.0) 

portfolio = solvers.qp(S, -pbar, G, h, A, b)['x'] 

print_portfolio(stock_list, portfolio)

但我得到这样的结果：

 AAPL   : 0.0000.
 IBM    : 0.8000.
 MSFT   : 0.0000.
 ORCL   : 0.2000.

所以不满足 x <= 20 的要求。可能是什么原因？

4

0 回答 0