Using loops inside NMaximize

*To*: mathgroup at smc.vnet.net*Subject*: [mg45399] Using loops inside NMaximize*From*: "Michael Harre" <Michael_Harre at resimac.com.au>*Date*: Tue, 6 Jan 2004 04:16:58 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com*Thread-index*: AcPT6Bn9hnZMriEnQOiam54UawH0GA==

I am trying to use NMaximize on a non-linear iterative function that conceptually looks like this: (*-------------------------------------------------------------------------*) variables = {x1, x2, <<96>>, x99, x100}; in1[[1]] = initial value; in2[[1]] = some other initial value; out[ previousIn_, variable_] := a nonlinear function f[100Variables_] := ( Do[ in1[[i+1]] = out[in1[[i]], 100variables[[i]] ]; in2[[i+1]] = out[in2[[i]], 100variables[[i]] ], {i, 1, Length[100variables]}; ]; Last[in1-in2] ); (*Then try and optimise for the last element produced by f*) NMaximize[{f[variables], simple constraints}, variables] (*-------------------------------------------------------------------------*) Mathematica tries to compute this, but it gets progressively slower and slower, so far it hasn't finished one Do loop given 12 hrs to run. If I abort the program and look at what it has already been produced, I see that Mathematica retains the whole nested function in an unevaluated form (i.e. expressed in terms of the variables), which very quickly becomes too large for my computer to handle. If I try to evaluate f[] using actual numbers, it generates an answer very quickly (approx. 0.3 secs). It looks as though I need some way for NMaximize to actually pass and immediately evaluate trial solutions, rather than trying to expand the entire expression before passing trial values (at least I think that's what's happening). The same thing happens using FindMaximum. Any suggestions as to how I can make this work? Cheers, Mike.