У меня есть код ниже, в нем я пытаюсь найти максимальное решение sharpe_ratio для эффективной границы. Я адаптировал код, который использовал ранее для решения задачи о рюкзаке в качестве mip. Я использую модуль cvxpy. Когда я запускаю код, сначала получаю повторяющиеся предупреждения. тогда он выходит из строя с ошибкой:

цикл ufunc не поддерживает аргумент 0 типа MulExpression, у которого нет вызываемого метода sqrt

Я включил код ниже. Я также включил предупреждение и ошибку. Ниже я привел образцы данных. Может ли кто-нибудь увидеть, в чем может быть проблема, и предложить, как ее исправить?

код:

selection = cvxpy.Variable(len(weights), boolean=True)


# The sum of the weights should be less than or equal to P
weight_constraint = weights * selection <= current_account



def portfolio_performance(weights, mean_returns, cov_matrix,period):
    
    print('returns')

    returns = np.sum(weights*mean_returns.T)*period

    print('std')
    std = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights))) * np.sqrt(period)
    return std, returns

def sharpe_ratio(weights, mean_returns, cov_matrix, risk_free_rate,period):
    p_var, p_ret = portfolio_performance(weights, mean_returns, cov_matrix,period)
    return (p_ret - risk_free_rate) / p_var




df=extended_prices

mean_returns = df.mean()
cov_matrix = df.cov()
risk_free_rate = 0.0





# Our total utility is the sum of the item utilities
# total_utility = utilities * selection

total_utility = sharpe_ratio(weights=selection, 
                             mean_returns=mean_returns, 
                             cov_matrix=cov_matrix,
                             risk_free_rate=risk_free_rate,
                            period=df.shape[0])



# We tell cvxpy that we want to maximize total utility 
# subject to weight_constraint. All constraints in 
# cvxpy must be passed as a list
knapsack_problem = cvxpy.Problem(cvxpy.Maximize(total_utility), [weight_constraint])

# Solving the problem
knapsack_problem.solve(solver=cvxpy.GLPK_MI)

предупреждение:

UserWarning: 
This use of ``*`` has resulted in matrix multiplication.
Using ``*`` for matrix multiplication has been deprecated since CVXPY 1.1.
    Use ``*`` for matrix-scalar and vector-scalar multiplication.
    Use ``@`` for matrix-matrix and matrix-vector multiplication.
    Use ``multiply`` for elementwise multiplication.

ошибка:

AttributeError                            Traceback (most recent call last)
AttributeError: 'MulExpression' object has no attribute 'sqrt'

The above exception was the direct cause of the following exception:

TypeError                                 Traceback (most recent call last)
<ipython-input-122-35839b05103e> in <module>
     49                              cov_matrix=cov_matrix,
     50                              risk_free_rate=risk_free_rate,
---> 51                             period=df.shape[0])
     52 
     53 

<ipython-input-122-35839b05103e> in sharpe_ratio(weights, mean_returns, cov_matrix, risk_free_rate, period)
     26 
     27 def sharpe_ratio(weights, mean_returns, cov_matrix, risk_free_rate,period):
---> 28     p_var, p_ret = portfolio_performance(weights, mean_returns, cov_matrix,period)
     29     return (p_ret - risk_free_rate) / p_var
     30 

<ipython-input-122-35839b05103e> in portfolio_performance(weights, mean_returns, cov_matrix, period)
     22 #         returns = 5
     23     print('std')
---> 24     std = np.sqrt(np.dot(weights.T, np.dot(cov_matrix, weights))) * np.sqrt(period)
     25     return std, returns
     26 

TypeError: loop of ufunc does not support argument 0 of type MulExpression which has no callable sqrt method

вес:

[171.35499572753906, 108.7699966430664, 104.56999969482422, 271.70001220703125, 253.1499938964844, 79.58999633789062, 479.6099853515625, 92.48999786376952, 152.24000549316406, 20.6299991607666, 159.17999267578125, 184.97999572753903, 41.2599983215332, 61.889997482299805, 82.5199966430664, 103.14999580383301, 123.77999496459961, 144.4099941253662, 165.0399932861328, 185.6699924468994]

образец данных:

print(df[:50])

          MMM         ABT        ABBV        ABMD         ACN       ATVI  \
0   175.869995  107.610001  103.809998  264.899994  248.520004  76.190002   
1   175.714996  107.355003  103.889999  265.589996  248.429993  76.690002   
2   176.135696  107.330002  104.010002  265.720001  249.085007  76.870003   
3   175.979996  107.415001  104.080002  265.910004  248.845001  77.010002   
4   176.350006  107.500000  103.849998  264.160004  249.603195  76.900002   
5   176.240005  107.245003  103.830002  262.910004  249.520004  76.629997   
6   176.700699  106.940002  103.839996  262.954987  249.100006  76.110001   
7   176.154999  106.820000  103.846497  262.595001  249.380005  76.339996   
8   176.550003  107.029999  103.955002  264.269989  249.645004  76.379997   
9   176.360001  106.809998  103.879997  263.559998  250.220001  76.430000   
10  176.804993  106.839996  103.824997  263.179993  250.139999  76.190002   
11  176.955002  106.699997  103.919998         NaN  249.520004  76.125000   
12  177.130005  106.684998  103.914597  263.209991  249.904999  76.019997   
13  176.860001  106.394997  103.769997  262.945007  249.869995  75.974998   
14  176.630005  106.500000  103.800003  262.850006  249.509995  76.070000   
15  176.580002  106.570000  103.930000  262.549988  249.770004  76.264000   
16  176.570007  106.605003  103.870003  262.399994  249.970001  76.059998   
17  176.690002  106.599998  103.860001  261.804993  249.410004  76.040001   
18  176.520004  106.790001  103.930000  261.929993  249.750000  76.074997   
19  176.845001  106.610001  103.959999  262.070007  249.279999  75.980003   
20  176.660004  106.599998  103.955002  261.575012  248.865005  76.029999   
21  176.550003  106.699997  103.870003  262.505005  248.850006  76.089996   
22  176.500000  106.660004  103.769997         NaN  248.940002  76.110001   
23  176.309998  106.669998  103.680000  262.200012  248.699997  76.250000   
24  176.315994  106.724998  103.690002  262.200012  249.020004  76.449997   
25  176.315002  106.690002  103.660004         NaN  249.065002  76.297600   
26  176.279999  106.510002  103.698997         NaN  248.809998  76.360001   
27  176.424606  106.543198  103.690002  262.595001  248.940002  76.339996   
28  176.660004  106.612900  103.739998         NaN  248.931793  76.279999   
29  176.722794  106.500000  103.660004  263.070007  249.149994  76.339996   
30  176.570007  106.419998  103.680000  263.690002  249.289993  76.535004   
31  176.686996  106.459999  103.794998  264.470001  249.330002  76.500000   
32  176.350006  106.433998  103.760002  264.260010  249.384995  76.559998   
33  176.369995  106.699997  103.629997         NaN  249.509995  76.519997   
34  176.160004  106.540001  103.709999  263.910004  249.369995  76.459999   
35  176.037598  106.332001  103.669998         NaN  249.050003  76.485001   
36  175.919998  106.379997  103.614998  264.209991  249.410004  76.480003   
37  175.899994  106.239998  103.730003  264.209991  249.429993  76.440002   
38  176.490005  106.160004  103.892700  264.200012  249.910004  76.290001   
39  176.509995  106.260002  103.949997  264.584991  249.970001  76.385002   
40  176.289993  106.459999  103.809998  264.559998  249.839996  76.440002   
41  176.619995  106.519997  103.910004         NaN  249.919998  76.320000   
42  176.350006  106.410004  103.830002  264.609985  250.009995  76.290001   
43  176.350006  106.425003  103.860001  264.540009  249.985001  76.260002   
44  176.270004  106.339996  103.870003  264.785004  249.860001  76.199898   
45  176.179993  106.360001  103.860001  264.500000  249.899994  76.106300   
46  176.205002  106.360001  103.834999  264.179993  249.759995  76.139999   
47  176.119995  106.389999  103.820000  264.519989  249.645004  76.120003   
48  176.251999  106.195000  103.800003  264.670013  249.740005  76.137802   
49  176.300003  106.239998  103.750000  264.839996  249.589996  76.114998   

          ADBE        AMD         AAP        AES      ATVI_2       AMD_2  \
0   467.489990  86.769997  150.009995  21.125000  152.380005  173.539993   
1   470.070007  87.209999  149.005005  21.004999  153.380005  174.419998   
2   469.512085  87.220001  148.613098  21.000000  153.740005  174.440002   
3   468.850006  87.070000  148.529999  21.020000  154.020004  174.139999   
4   470.535004  87.550003  148.865005  21.075001  153.800003  175.100006   
5   470.410004  87.550102  148.830002  21.010000  153.259995  175.100204   
6   468.819885  87.129997  147.990005  20.995001  152.220001  174.259995   
7   469.279999  86.714897  148.070007  20.940001  152.679993  173.429794   
8   469.070007  87.078102  148.529999  20.990000  152.759995  174.156204   
9   469.459991  86.820000  148.369995  20.955000  152.860001  173.639999   
10  468.929993  86.739899  148.250000  21.010000  152.380005  173.479797   
11  466.700012  86.419998  148.190002  20.973499  152.250000  172.839996   
12  466.329987  86.339996  148.339996  21.040001  152.039993  172.679993   
13  467.734985  86.519997  148.550003  20.940001  151.949997  173.039993   
14  466.630005  86.110001  148.270004  20.940001  152.139999  172.220001   
15  467.480011  86.180000  147.669998  20.870001  152.528000  172.360001   
16  467.075012  85.889999  147.539993  20.840000  152.119995  171.779999   
17  467.070007  85.980003  147.384995  20.834999  152.080002  171.960007   
18  468.390015  86.199898  147.479996  20.875000  152.149994  172.399796   
19  467.600006  86.309998  147.570999  20.915001  151.960007  172.619995   
20  468.369995  86.520103  147.804993  20.889999  152.059998  173.040207   
21  467.644989  86.431999  147.850006  20.934999  152.179993  172.863998   
22  467.480011  86.363297  148.335007  20.934999  152.220001  172.726593   
23  467.750000  86.410004  148.735001  20.969999  152.500000  172.820007   
24  468.375000  86.529999  148.682999  21.019899  152.899994  173.059998   
25  467.540009  86.211700  148.360001  21.075001  152.595200  172.423401   
26  466.230011  86.075600  148.735001  21.080000  152.720001  172.151199   
27  466.200012  86.139397  148.820007  21.063299  152.679993  172.278793   
28  466.359985  86.121696  149.179993  21.098000  152.559998  172.243393   
29  466.440002  86.184998  149.414993  21.084999  152.679993  172.369995   
30  467.220001  86.260002  149.639999  21.090000  153.070007  172.520004   
31  466.920013  86.309998  149.770004  21.129999  153.000000  172.619995   
32  467.579987  86.364998  149.365005  21.155001  153.119995  172.729996   
33  467.890015  86.514397  149.580002  21.115000  153.039993  173.028793   
34  468.174988  86.565002  149.595001  21.075001  152.919998  173.130005   
35  467.820007  86.540001  149.330002  21.059999  152.970001  173.080002   
36  467.589996  86.660004  149.330002  21.049999  152.960007  173.320007   
37  467.530090  86.620003  149.990005  21.030001  152.880005  173.240005   
38  467.070007  86.940002  149.460007  21.030001  152.580002  173.880005   
39  466.899994  87.050003  149.740005  20.950100  152.770004  174.100006   
40  466.660004  87.124397  149.559998  20.915001  152.880005  174.248795   
41  466.899994  87.203400  149.589996  20.969999  152.639999  174.406799   
42  468.149994  87.279999  149.710007  20.969999  152.580002  174.559998   
43  469.116211  87.264999  149.839996  20.995001  152.520004  174.529999   
44  469.210785  87.235001  149.850006  20.920000  152.399796  174.470001   
45  469.052795  87.370003  149.839996  20.910000  152.212601  174.740005   
46  469.279999  87.309998  150.100006  20.940001  152.279999  174.619995   
47  468.655304  87.080002  150.014999  20.959999  152.240005  174.160004   
48  468.570007  87.040001  150.220001  20.959999  152.275604  174.080002   
49  469.649994  87.085098  150.270004  20.940001  152.229996  174.170197   

        AES_2      AES_3      AES_4       AES_5       AES_6       AES_7  \
0   42.250000  63.375000  84.500000  105.625000  126.750000  147.875000   
1   42.009998  63.014997  84.019997  105.024996  126.029995  147.034994   
2   42.000000  63.000000  84.000000  105.000000  126.000000  147.000000   
3   42.040001  63.060001  84.080002  105.100002  126.120003  147.140003   
4   42.150002  63.225002  84.300003  105.375004  126.450005  147.525005   
5   42.020000  63.030001  84.040001  105.050001  126.060001  147.070002   
6   41.990002  62.985003  83.980003  104.975004  125.970005  146.965006   
7   41.880001  62.820002  83.760002  104.700003  125.640003  146.580004   
8   41.980000  62.969999  83.959999  104.949999  125.939999  146.929998   
9   41.910000  62.865000  83.820000  104.775000  125.730000  146.684999   
10  42.020000  63.030001  84.040001  105.050001  126.060001  147.070002   
11  41.946999  62.920498  83.893997  104.867496  125.840996  146.814495   
12  42.080002  63.120003  84.160004  105.200005  126.240005  147.280006   
13  41.880001  62.820002  83.760002  104.700003  125.640003  146.580004   
14  41.880001  62.820002  83.760002  104.700003  125.640003  146.580004   
15  41.740002  62.610003  83.480003  104.350004  125.220005  146.090006   
16  41.680000  62.520000  83.360001  104.200001  125.040001  145.880001   
17  41.669998  62.504997  83.339996  104.174995  125.009995  145.844994   
18  41.750000  62.625000  83.500000  104.375000  125.250000  146.125000   
19  41.830002  62.745003  83.660004  104.575005  125.490005  146.405006   
20  41.779999  62.669998  83.559998  104.449997  125.339996  146.229996   
21  41.869999  62.804998  83.739998  104.674997  125.609997  146.544996   
22  41.869999  62.804998  83.739998  104.674997  125.609997  146.544996   
23  41.939999  62.909998  83.879997  104.849997  125.819996  146.789995   
24  42.039799  63.059698  84.079597  105.099497  126.119396  147.139296   
25  42.150002  63.225002  84.300003  105.375004  126.450005  147.525005   
26  42.160000  63.240000  84.320000  105.400000  126.480000  147.559999   
27  42.126598  63.189898  84.253197  105.316496  126.379795  147.443094   
28  42.195999  63.293999  84.391998  105.489998  126.587997  147.685997   
29  42.169998  63.254997  84.339996  105.424995  126.509995  147.594994   
30  42.180000  63.270000  84.360001  105.450001  126.540001  147.630001   
31  42.259998  63.389997  84.519997  105.649996  126.779995  147.909994   
32  42.310001  63.465002  84.620003  105.775003  126.930004  148.085005   
33  42.230000  63.344999  84.459999  105.574999  126.689999  147.804998   
34  42.150002  63.225002  84.300003  105.375004  126.450005  147.525005   
35  42.119999  63.179998  84.239998  105.299997  126.359997  147.419996   
36  42.099998  63.149998  84.199997  105.249996  126.299995  147.349995   
37  42.060001  63.090002  84.120003  105.150003  126.180004  147.210005   
38  42.060001  63.090002  84.120003  105.150003  126.180004  147.210005   
39  41.900200  62.850300  83.800400  104.750500  125.700600  146.650700   
40  41.830002  62.745003  83.660004  104.575005  125.490005  146.405006   
41  41.939999  62.909998  83.879997  104.849997  125.819996  146.789995   
42  41.939999  62.909998  83.879997  104.849997  125.819996  146.789995   
43  41.990002  62.985003  83.980003  104.975004  125.970005  146.965006   
44  41.840000  62.760000  83.680000  104.600000  125.520000  146.440001   
45  41.820000  62.730000  83.639999  104.549999  125.459999  146.369999   
46  41.880001  62.820002  83.760002  104.700003  125.640003  146.580004   
47  41.919998  62.879997  83.839996  104.799995  125.759995  146.719994   
48  41.919998  62.879997  83.839996  104.799995  125.759995  146.719994   
49  41.880001  62.820002  83.760002  104.700003  125.640003  146.580004   

         AES_8       AES_9  
0   169.000000  190.125000  
1   168.039993  189.044992  
2   168.000000  189.000000  
3   168.160004  189.180004  
4   168.600006  189.675007  
5   168.080002  189.090002  
6   167.960007  188.955008  
7   167.520004  188.460005  
8   167.919998  188.909998  
9   167.639999  188.594999  
10  168.080002  189.090002  
11  167.787994  188.761494  
12  168.320007  189.360008  
13  167.520004  188.460005  
14  167.520004  188.460005  
15  166.960007  187.830008  
16  166.720001  187.560001  
17  166.679993  187.514992  
18  167.000000  187.875000  
19  167.320007  188.235008  
20  167.119995  188.009995  
21  167.479996  188.414995  
22  167.479996  188.414995  
23  167.759995  188.729994  
24  168.159195  189.179094  
25  168.600006  189.675007  
26  168.639999  189.719999  
27  168.506393  189.569693  
28  168.783997  189.881996  
29  168.679993  189.764992  
30  168.720001  189.810001  
31  169.039993  190.169992  
32  169.240005  190.395006  
33  168.919998  190.034998  
34  168.600006  189.675007  
35  168.479996  189.539995  
36  168.399994  189.449993  
37  168.240005  189.270006  
38  168.240005  189.270006  
39  167.600800  188.550900  
40  167.320007  188.235008  
41  167.759995  188.729994  
42  167.759995  188.729994  
43  167.960007  188.955008  
44  167.360001  188.280001  
45  167.279999  188.189999  
46  167.520004  188.460005  
47  167.679993  188.639992  
48  167.679993  188.639992  
49  167.520004  188.460005 

Я попытался обновить свою исходную целевую функцию, как показано ниже, чтобы сделать ее совместимой с dcp, но теперь я получаю сообщение об ошибке ниже. может кто-нибудь указать, что я делаю не так?

Обновлять:

nonzero_constraint = selection.T * (mean_returns) ›= 1

total_utility = selection.T cov_matrix selection

knapsack_problem = cvxpy.Problem (cvxpy.Minimize (total_utility), [weight_constraint, nonzero_constraint])

Вы не можете просто использовать функции, отличные от cvxpy, для cvxpy-объектов!

knapsack_problem.solve (решатель = cvxpy.GLPK_MI)

ошибка:

DCPError Traceback (последний вызов последним) в 76 77 # Решение проблемы --- ›78 knapsack_problem.solve (solver = cvxpy.GLPK_MI)

~ / anaconda3 / envs / pyopft / lib / python3.6 / site-packages / cvxpy / issues / problem.py в решении (self, * args, ** kwargs) 394 else: 395 resolve_func = Problem._solve - ›396 вернуть решение_func (self, * args, ** kwargs) 397 398 @classmethod

~ / anaconda3 / envs / pyopft / lib / python3.6 / site-packages / cvxpy / issues / problem.py в _solve (self, solver, warm_start, verbose, gp, qcp, requires_grad, enforce_dpp, ** kwargs) 749 750 данные, цепочка решений, inverse_data = self.get_problem_data (- ›751 solver, gp, enforce_dpp) 752 solution = resolve_chain.solve_via_data (753 self, data, warm_start, verbose, kwargs)

~ / anaconda3 / envs / pyopft / lib / python3.6 / site-packages / cvxpy / issues / problem.py в get_problem_data (self, solver, gp, enforce_dpp) 498 self._cache.invalidate () 499 resolve_chain = self._construct_chain (- ›500 solver = solver, gp = gp, enforce_dpp = enforce_dpp) 501 self._cache.key = key 502 self._cache.solving_chain = resolve_chain

~ / anaconda3 / envs / pyopft / lib / python3.6 / site-packages / cvxpy / issues / problem.py в _construct_chain (self, solver, gp, enforce_dpp) 657 кандидата_solvers = self._find_candidate_solvers (solver = solver, gp = gp ) 658 return construct_solving_chain (self, кандидата_solvers, gp = gp, - ›659 enforce_dpp = enforce_dpp) 660 661 def _invalidate_cache (self):

~ / anaconda3 / envs / pyopft / lib / python3.6 / site-packages / cvxpy / reductions / solvers / resolve_chain.py в construct_solving_chain (проблема, кандидаты, gp, enforce_dpp) 149 если len (problem.variables ()) == 0: 150 return SolvingChain (сокращение = [ConstantSolver ()]) - ›151 сокращение = _reductions_for_problem_class (проблема, кандидаты, gp) 152 153 dpp_context = 'dcp' если не gp else 'dgp'

~ / anaconda3 / envs / pyopft / lib / python3.6 / site-packages / cvxpy / reductions / solvers / Solvers_chain.py в _reductions_for_problem_class (проблема, кандидаты, gp) 88 Рассмотрите возможность вызова метода решения () с qcp=True.) 89 поднять ошибку DCPError ( --- ›90 Проблема не соответствует правилам DCP. В частности: \ n + append) 91 elif gp, а не проблема. Is_dgp (): 92 append = build_non_disciplined_error_msg (проблема, 'DGP')

Решение проблемы