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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


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