Use optimize.minimize from scipy with 2 variables and interpolated function

Question

I didn\'t find a way to perform optimize.minimize from scipy with a multidimensional function. In nearly all examples an analytical function is optimized while my function is in

Answer 1

One more possible solution (hope you get the idea):

One more function is created (f), and the minimized values are sent as arguments to this function.

from scipy.optimize import minimize

x = data.Height.values
y = data.Weight.values

def f(params):
    w0, w1 = params
    return mse(w0, w1, x, y)

optimum = minimize(f, (0,0), method = 'L-BFGS-B', bounds = ((-100, 100), (-5,5)) )
w0 = optimum.x[0]
w1 = optimum.x[1]

Also tried implementation with lambda function, but had no luck.

Answer 2

First, to find global maximum (instead of minimum) you need to interpolate your function with opposite sign:

F2 = interp2d(x, y, -z)

Second, the callable in minimize takes a tuple of arguments, and interp2d object needs input coordinates to be given as separate positional arguments. Therefore, we cannot use interp2d object in minimize directly; we need a wrapper that will unpack a tuple of arguments from minimize and feed it to interp2d:

f = lambda x: F2(*x)

And third, to use minimize you need to specify an initial guess for minimum (and bounds, in your case). Any reasonable point will do:

x0 = (2200, 12)
bounds = [(2000,3500),(10,50)]
print minimize(f, x0, method='SLSQP', bounds=bounds)

This yields:

  status: 0
 success: True
    njev: 43
    nfev: 243
     fun: array([-59.99999488])
       x: array([ 2500.00002708,    24.99999931])
 message: 'Optimization terminated successfully.'
     jac: array([ 0.07000017,  1.        ,  0.        ])
     nit: 43