Re: Efficient repeated use of FindRoot

• To: mathgroup at smc.vnet.net
• Subject: [mg74061] Re: [mg74049] Efficient repeated use of FindRoot
• From: "Michael A. Gilchrist" <mikeg at utk.edu>
• Date: Thu, 8 Mar 2007 04:35:34 -0500 (EST)
• References: <200703070816.DAA26723@smc.vnet.net>

```Hi Chris,

The basic answer is I am interested in understanding the lagrangian and I
think working with it is the best way to begin to understand it.  I've
also run into issues with NMinimize in the past.  In my experience,
NMinimize is more compuationally intensive than FindRoot or FindMinimum
for systems where there's a single global optimum as I would expect in
this case.  In addition, NMinimize is too 'blackbox' for me (i.e. I
understand the routines in FindRoot better).  As a result I don't feel
like I have as much control over it as I do FindRoot.

Also, from what I understand I'd be running into the same problem of the
large initialization time.

Mike

On Wed, 7 Mar 2007, Chris Chiasson wrote:

> Why are you not using NMinimize or NMaximize?
>
> On 3/7/07, Michael A. Gilchrist <mikeg at utk.edu> wrote:
>> Hi all,
>>
>> I've got an optimization problem that I am trying to evaluate numerically
>> and at a number of different points of a particular variable.  I am using
>> a Lagrangian multiplier to impose a constraint on the optimization of the
>> 'free variables' and as a result trying to find the root for a set of n
>> coupled equations (in its full form n = 4000+ variables).
>>
>>
>> Using some approximations I can come up with some reasonable initial
>> conditions, but, as you might imagine, it takes quite some time to run
>> the code.  Looking at the output it appears that the greatest amount of
>> time is initialization of the FindRoot routine (once the routine is
>> running it calculates each step quite quickly).
>>
>>
>> Here's some pseudo code to illustrate the basic idea:
>>
>> (*set up eqns and variables*)
>> Clear[m];
>> vars = Table[m[i], {1, n}]
>>
>> eqns = Table[
>>         (llik[i, vars] + \[Lambda] m[i] ==0), {i, 2, n}]
>>                                 (*llik previously defined)
>> ics =   Table[
>>          m0[i] = T[i]/phi[i] (*T[i] and Phi[i] previously defined*),
>>         {i, 2, n}];
>>
>> frvars = Table[{m[i], m0[i] * 0.01, m0[i]*10}, {i, 2, n}];
>>
>>
>> (*look for solution to problem for multiple values of m[1] *)
>> Table[
>>         FindRoot[eqns, frvars], {m[1], 0.01, 0.2, 0.01}]
>>
>>
>> I am aware of the NDSolve package StateData that allows one to
>> efficiently evaluate DE's with various different initial
>> conditions by processing the equations.
>>
>> I've looked through the documentation on FindRoot and haven't found a
>> similar routine/ability.  I'm wondering if anyone has any ideas on how
>> one might increase the efficiency of my calculations.
>>
>> Thanks.
>>
>> Mike
>>
>>
>> -----------------------------------------------------
>> Department of Ecology & Evolutionary Biology
>> 569 Dabney Hall
>> University of Tennessee
>> Knoxville, TN 37996-1610
>>
>> phone:(865) 974-6453
>> fax:  (865) 974-6042
>>
>> web: http://eeb.bio.utk.edu/gilchrist.asp
>> -----------------------------------------------------
>>
>>
>>
>
>
> --
> http://chris.chiasson.name/
>

-----------------------------------------------------
Department of Ecology & Evolutionary Biology
569 Dabney Hall
University of Tennessee
Knoxville, TN 37996-1610

phone:(865) 974-6453
fax:  (865) 974-6042

web: http://eeb.bio.utk.edu/gilchrist.asp
-----------------------------------------------------

```

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