python - scipy: minimize vs. minimize.scalar; return F versus return F**2; shouldnt make a difference? -

i found behavior cannot explain. miss ?

i have implicit function:

def my_cost_fun(x,a,b,c):     # x scalar; variables provided numpy arrays     f = some_fun(x,a,b,c) - x     return f 

i minimize function using:

• optimize.fsolve(my_cost_fun,0.2,args = (a,b,c))
• optimize.brentq(my_cost_fun,-0.2,0.2,args = (a,b,c))

or mimimize function:

• optimize.minimize(my_cost_fun,0.2,args = (a,b,c),method = 'l-bfgs-b',bounds=((0,a),)

the strange thing is:

• if use return f

  • brent_q method , fsolve give same result , %timeit measures fastest loop ~ 250 µs
  • l-bfgs-b (and slsqp , tnc) not change x0 @ , provides wrong result

• if use return f**2:

  • fsolve returns right solution converges slowly; 1.2 ms fastest loop

  • l-bfgs-b returns right solution converges slowly: 1.5 ms fastest loop

can explain why ?

as mentioned in comments:

here 1 possible explaination of why l-bfgs-b not working when use return f: if value of f can negative, optmize.minimize try find negative value can. minimize isn't finding root, it's finding minimum. if return f**2 instead, since real-valued functions f**2 positive, minima of f**2 happen @ f=0, i.e. minima roots.

this doesn't explain timing issue, may of secondary concern. still curious study timing particular some_fun(x,a,b,c) if chance post definition.