使用python scipy.optimize.minimize优化具有许多输出的函数

Question

I've been searching a little in the web and I did not found any solution to this question, so I decided to formally ask here.

I have a function that has multiple outputs:

f(input1,input2,... ,inputn) = output1,ouput2,output3

My wish is to minimize output1 constraining other outputs, for instance:

output2 >= 0 and output3 <= 7   (*constraints*)

My idea was to have the following program structure:

def function(input1,input2,...,inputn):
    #very secret part of code
    return(output1,ouput2,output3)

inputs=[1,31,22]
_res = optimize.minimize(function, inputs,  method='nelder-mead', 
options=options,*constraints*)

Now I believe that the answer should be in the documentation of the Scipy minimize function.

The fact is that, from what I've understood, I can only constrain my function inputs and not some of the outputs of my function. Am I missing something?

Answer 1

Here is an example of optimization with constraint:

from scipy.optimize import minimize

def f(xy):
    x, y = xy 
    return x**2 + y**2

def constraint1(xy):
    x, y = xy 
    return x-1

def constraint2(xy):
    x, y = xy 
    return y-2

constraints = ({'type': 'ineq', 'fun': constraint1},
               {'type': 'ineq', 'fun': constraint2})

xy_start = [0, 0]
res = minimize(f, xy_start, method='SLSQP', constraints=constraints)

which gives:

     fun: 4.999999999999997
     jac: array([2., 4.])
 message: 'Optimization terminated successfully.'
    nfev: 13
     nit: 3
    njev: 3
  status: 0
 success: True
       x: array([1., 2.])

The idea is that your function you want to minimize is well scalar: the returned value have to be only output1 . Additional functions have to be added in order to define each constraint: constraint1(inputs)->output2 , constraint2(inputs)->output3 ... etc

Maybe you could separate the 'very secret part' of your code into different functions, which will be used both by the objective function and by the constraints functions