python - error using L-BFGS-B in scipy -

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i puzzling result when using 'l-bfgs-b' method in scipy.optimize.minimize:

import scipy.optimize optimize import numpy np  def testfun():     prec = 1e3      func0 = lambda x: (float(x[0]*prec)/prec+0.5)**2+(float(x[1]*prec)/prec-0.3)**2     func1 = lambda x: (float(round(x[0]*prec))/prec+0.5)**2+(float(round(x[1]*prec))/prec-0.3)**2      result0 = optimize.minimize(func0, np.array([0,0]), method = 'l-bfgs-b', bounds=((-1,1),(-1,1)))     print result0     print 'func0 @ [0,0]:',func0([0,0]),'; func0 @ [-0.5,0.3]:',func0([-0.5,0.3]),'\n'      result1 = optimize.minimize(func1, np.array([0,0]), method = 'l-bfgs-b', bounds=((-1,1),(-1,1)))     print result1     print 'func1 @ [0,0]:',func1([0,0]),'; func1 @ [-0.5,0.3]:',func1([-0.5,0.3])  def main():     testfun()

func0() , func1() identical quadratic functions precision difference of 0.001 input values. 'l-bfgs-b' method works func0. however, adding round() function in func1(), 'l-bfgs-b' stops search optimal values after first step , directly use initial value [0,0] optimal point.

this not restricted round(). replace round() in func1() int() results in same error.

does know reason this?

thanks lot.

bfgs method 1 of method relies on not function value, gradient , hessian (think of first , second derivative if wish). in func1(), once have round() in it, gradient no longer continuous. bfgs method therefore fails right after 1st iteration (think of this: bfgs searched around starting parameter , found gradient not changed, stopped). similarly, expect other methods requiring gradient fail bgfs.

you may able working precondition or rescaling x. better yet, should try gradient free method such 'nelder-mead' or 'powell'


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