scipy.optimize.linprog 等式约束不满足

Question

I am currently trying to solve a LP optimization problem using scipy.optimize.linprog.

I triple checked the whole code but I am not able to understand why the only equality constraint of the problem is not satisfied.

import numpy as np
import scipy.optimize as opt
import scipy.stats as sts
import pandas as pd
    
def problems(a, t, alpha):
    #
    y = []
    
    for i in a.columns:
        loc, scale = sts.gumbel_l.fit(a[i])
        y.append(sts.gumbel_l.rvs(loc, scale, t))
    
    obj = [1] + [0 for x in range(len(a.columns))] + [(1 / (1 - alpha) * t) for x in range(t)]
    
    ttt = np.zeros((t, t))
    np.fill_diagonal(ttt, 1.)
    
    aub = np.concatenate((np.asmatrix([1 for x in range(t)]).T, np.asmatrix(y).T, ttt), axis = 1)
    aeq = np.asmatrix(([0] + [1 for x in range(len(a.columns))] + [0 for x in range(t)]))
    
    bub = [0. for x in range(t)]
    beq = [1.]
    
    res = opt.linprog(
        c = obj, 
        A_ub = aub,
        b_ub = bub,
        A_eq = aeq,
        b_eq = beq,
    )

    return res['x']
    
if __name__ == "__main__":
    np.random.seed(2)
    a = pd.DataFrame(np.random.rand(400, 3))
    res = problems(a, t = 100, alpha = 0.95)
    print(res.round(3))

Please note that this Is a three variable optimization problem:

obj = [1] + [0 for x in range(len(a.columns))] + [(1 / (1 - alpha) * t) for x in range(t)]

Specifically I need that after the optimization the sum of the elements of the second variable that needs to be determined (which is an array of len(a.columns)) is equale to 1. Hence the equality constraint defined by aeq and bee`.

Unfortunately the result is the following (2.013 + 1.573 + 2.413 is not equal to 1.):

[0.661 2.013 1.573 2.413 1.995 2.038 0.695 1.975 1.056 2.202 1.728 1.494
 1.214 1.419 1.382 1.632 1.36  1.004 1.283 2.314 2.286 1.651 0.929 1.834
 1.663 1.346 2.34  2.09  1.831 1.886 1.845 2.222 2.318 2.064 1.242 1.632
 0.33  1.77  0.687 0.618 0.07  1.148 1.939 2.08  2.18  1.143 2.051 0.616
 1.396 1.027 0.978 1.014 1.038 1.62  0.999 2.103 1.639 2.198 2.445 2.171
 0.862 1.556 0.608 1.465 1.372 2.143 0.738 1.99  1.525 1.344 1.798 2.111
 1.168 2.331 2.082 1.248 2.27  1.738 1.936 1.957 0.661 1.783 1.509 0.522
 1.785 2.095 1.537 2.229 1.065 1.973 2.193 0.132 1.997 0.984 1.359 1.761
 1.809 0.247 1.893 2.04  1.873 2.019 2.124 2.107]

Answer 1

The documentation asks for:

A_ub: 2-D array, optional

A_eq: 2-D array, optional

You use np.matrix -> read the note!

Base your code on numpy's array-type

(which is more than just copy-paste -> this also somewhat indicates, what possibly could go wrong inside of linprog).