Re: Minimization Algebraically
- To: mathgroup at smc.vnet.net
- Subject: [mg103398] Re: Minimization Algebraically
- From: Peter Pein <petsie at dordos.net>
- Date: Sun, 20 Sep 2009 06:21:24 -0400 (EDT)
- References: <h8vkeh$8un$1@smc.vnet.net>
Bayers, Alexander schrieb:
> I am currently trying to minimize the following function in Mathematica:
>
> ((360*(-1 + E^(0.2493150684931507*r0)))/91 - r[L3m])^2
>
> Using r0. When I try to minimize this algebraically using Minimize,
> however, I receive the following answer:
>
> Minimize[((360*(-1 + E^(0.2493150684931507*r0)))/91 - r[L3m])^2, {r0}]
>
> Instead of an algebraic answer. Is there any way to coerce Mathematica
> to return the algebraic answer through a call to minimize?
>
> Thanks,
>
> Alex
>
>
Guessing that all quantities starting with "r" shall be nonnegative:
Build the 0th, 1st and 2nd derivative w.r.t. r0:
In[1]:= deriv = NestList[D[#1, r0] & ,
((360/91)*(-1 + E^((91*r0)/365)) - r[L3m])^2,
2];
Solve "first derivative" == 0 :
In[2]:= candidate =
Cases[Reduce[deriv[[2]] == 0 <= r0, r0] /. And | Or -> List,
_Equal, Infinity] /. Equal -> Rule
Out[2]= {r0 -> (365/91)*Log[(1/360)*(360 + 91*r[L3m])]}
and check if the 2nd deriv. is positive:
In[3]:= Simplify[deriv[[3]] > 0 /. candidate, r[L3m] >= 0]
Out[3]= True