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