How to express a quadratic objective in Docplex on python

Question

If any one could help,I can't express the objective function, this is my code:

import numpy as np
def portfolio_return( weights, returns):
    return weights.T @ returns

def portfolio_vol( weights, covmatrix):
    return np.sqrt(weights.T @ covmatrix @ weights)

def sharp_ratio(er,covmat,w,rf = 0.01):
    r_p = portfolio_return(w, er)/100
    sigma_p = portfolio_vol(w,cov)/100
    return (r_p-rf)/sigma_p

w = mdl.integer_var_list(5,5,30, 'w')
mdl.add_constraint(mdl.sum(w) == 100)
mdl.minimize(-sharp_ratio(quartered_er, cov,np.array(w)))

But i get this error:

loop of ufunc does not support argument 0 of type QuadExpr which has no callable sqrt method

Answer 1

You may use numpy for some computation after the solve but the constraints should be described with functions from docplex.

For instance, the quadratic example from the making optimization easy with python story

from docplex.mp.model import Model

mdl = Model(name='buses')
nbbus40 = mdl.integer_var(name='nbBus40')
nbbus30 = mdl.integer_var(name='nbBus30')
mdl.add_constraint(nbbus40*40 + nbbus30*30 >= 300, 'kids')
mdl.minimize(nbbus40**2*500 + nbbus30**2*400)

mdl.solve()

for v in mdl.iter_integer_vars():
    print(v," = ",v.solution_value)

import numpy as np
print("We bring ",np.array(
    [40,30])@np.array([nbbus40.solution_value,nbbus30.solution_value])
      ," kids to the zoo")

gives

nbBus40  =  4.0
nbBus30  =  5.0
We bring  310.0  kids to the zoo