Error specifying constraints in scipy.optimize.fmin_cobyla for parameter estimation

Question

I'm using python 2.7 in Canopy and I'm trying to fit 6 parameters of a model by minimising mean squared error between data and model predictions. I'm using COBYLA since I need bounds on parameter values, and I don't have a gradient.

Currently, I have:

import numpy as np
import scipy.optimize as opt

def cost_func(pars,y,x):
    y_hat = model_output(pars,x)
    mse = np.mean((y-y_hat)**2)
    return mse

def make_constraints(par_min,par_max):
    cons = []    
    for (i,(a,b)) in enumerate(zip(par_min,par_max)):
        lower = lambda x: x[i] - a
        upper = lambda x: b - x[i]
        cons = cons + [lower] + [upper]
    return cons

def estimate_parameters(par_min, par_max,par_init,x,y):
    cons = make_constraints(par_min,par_max)
    opt_pars = opt.fmin_cobyla(cost_func,pars,cons,args=([y,x]))
    return opt_pars

However I get the error:

---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-63-9e84e10303e1> in <module>()
----> 1 opt_pars = estimate_parameters(par_min,par_max,par_init,x,y)

<ipython-input-61-f38615d82ee5> in estimate_parameters(par_min,par_max,par_init,x,y)
      9     cons = make_constraints(par_min,par_max)
     10 
---> 11     opt_pars = opt.fmin_cobyla(cost_func,par_init,cons,args=([y,x]))
     12     return opt_pars 

/home/luke/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/optimize/cobyla.pyc in fmin_cobyla(func, x0, cons, args, consargs, rhobeg, rhoend, iprint, maxfun, disp, catol)
    169 
    170     sol = _minimize_cobyla(func, x0, args, constraints=con,
--> 171                            **opts)
    172     if iprint > 0 and not sol['success']:
    173         print("COBYLA failed to find a solution: %s" % (sol.message,))

/home/luke/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/optimize/cobyla.pyc in _minimize_cobyla(fun, x0, args, constraints, rhobeg, tol, iprint, maxiter, disp, catol, **unknown_options)
    244     xopt, info = _cobyla.minimize(calcfc, m=m, x=np.copy(x0), rhobeg=rhobeg,
    245                                   rhoend=rhoend, iprint=iprint, maxfun=maxfun,
--> 246                                   dinfo=info)
    247 
    248     if info[3] > catol:

/home/luke/Enthought/Canopy_64bit/User/lib/python2.7/site-packages/scipy/optimize/cobyla.pyc in calcfc(x, con)
    238         f = fun(x, *args)
    239         for k, c in enumerate(constraints):
--> 240             con[k] = c['fun'](x, *c['args'])
    241         return f
    242 

TypeError: <lambda>() takes exactly 1 argument (3 given)

This error isn't totally clear to me, but my understanding is that 3 arguments are being passed to my constraint functions. However, I can't work out where these 3 arguments are coming from.

I've looked at other stackoverflow questions about this and taken what I can from them, but I am still having this problem

Specifying constraints for fmin_cobyla in scipy

Python SciPy: optimization issue fmin_cobyla : one constraint is not respected

Python: how to create many constraints for fmin_cobyla optimization using lambda functions

Answer 1

If the argument consargs of fmin_cobyla is None, the constraint functions are also passed *args, where args is the argument given to fmin_cobyla. To pass no additional arguments to the constraint functions, use consargs=().

Alternatively, in the function make_constraints, change this

        lower = lambda x: x[i] - a
        upper = lambda x: b - x[i]

to

        lower = lambda x, *args: x[i] - a
        upper = lambda x, *args: b - x[i]