Re: Efficient repeated use of FindRoot

*To*: mathgroup at smc.vnet.net*Subject*: [mg74067] Re: [mg74049] Efficient repeated use of FindRoot*From*: "Chris Chiasson" <chris at chiasson.name>*Date*: Thu, 8 Mar 2007 04:38:56 -0500 (EST)*References*: <200703070816.DAA26723@smc.vnet.net>

You have hit the nail exactly on the head. NMinimize uses optimization techniques that are less efficient than those of FindMinimum if the global optimum can be found by using local (derivative) information from a chosen starting point. Until FindMinimum sprouts a constraint handling feature, we are left to fill the gap. I will think about your problem a bit more. On 3/7/07, Michael A. Gilchrist <mikeg at utk.edu> wrote: > 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 > ----------------------------------------------------- > > -- http://chris.chiasson.name/

**References**:**Efficient repeated use of FindRoot***From:*"Michael A. Gilchrist" <mikeg@utk.edu>