Problems and questions regarding scipy.optimize.minimize in Python -

i have questions , problems regarding scipy's optimize.minimize routine. minimize function:

f(eta) = sum_i |eta*x_i - y_i|

with regard eta. since not familiar minimize routine , corresponding methods, tried out. however, using method bfgs raises following error:

file "/usr/local/lib/python3.4/dist-packages/scipy/optimize/_minimize.py", line 441, in minimize return _minimize_bfgs(fun, x0, args, jac, callback, **options) file "/usr/local/lib/python3.4/dist-packages/scipy/optimize/optimize.py", line 904, in _minimize_bfgs a1 = - sk[:, numpy.newaxis] * yk[numpy.newaxis, :] * rhok indexerror: 0-d arrays can use single () or list of newaxes (and single ...) index 

which not able solve. please find code, causes error below. using python3 scipy 0.17.0 , numpy 1.8.2 on ubuntu 14.04.3 lts.

furthermore, method conjugate gradient seems perform worse other methods.

last not least, favour estimating minimum finding 0 of first derivative via scipy.optimize.brentq. fine or recommend approach? prefer robustness on speed.

here code illustrating problems , questions:

from scipy import optimize import numpy np  def function(x, bs, cs):     sum = 0.     b, c in zip(bs, cs):         sum += np.abs(x*b - c)     return sum  def derivativefunction(x, bs, cs):     sum = 0.     b, c in zip(bs, cs):         if x*b > c:             sum += b         else:             sum -= b     return sum  np.random.seed(1000) bs = np.random.rand(10) cs = np.random.rand(10)  eta0 = 0.5  res = optimize.minimize(fun=function, x0=eta0, args=(bs, cs), method='nelder-mead', tol=1e-6) print('nelder-mead:\t', res.x[0], function(res.x[0], bs, cs))  res = optimize.minimize(fun=function, x0=eta0, args=(bs, cs,),  method='cg', jac=derivativefunction, tol=1e-6) print('cg:\t', res.x[0], function(res.x[0], bs, cs))  x = optimize.brentq(f=derivativefunction, a=0, b=2., args=(bs, cs), xtol=1e-6, maxiter=100)  print('brentq:\t', x, function(x, bs, cs))  #throwing error res = optimize.minimize(fun=function, x0=eta0, args=(bs, cs), method='bfgs', jac=derivativefunction, tol=1e-6) print('bfgs:\t', res.x[0], function(res.x[0], bs, cs)) 

its output is:

nelder-mead:     0.493537902832 3.71986334101 cg:  0.460178525461 3.72659733011 brentq:  0.49353725172947666 3.71986347245 

where first value position of minimum , second value minimum itself. output misses error message above.

thank help!