Optimization doing more function evaluations than claimed?

*To*: mathgroup at smc.vnet.net*Subject*: [mg57197] Optimization doing more function evaluations than claimed?*From*: Gareth Russell <gjr2008 at columbia.edu>*Date*: Fri, 20 May 2005 04:43:46 -0400 (EDT)*Organization*: Columbia University*Sender*: owner-wri-mathgroup at wolfram.com

Hi All, I have been using FindMaximize without symbolic derivatives to maximize a likelihood function that operates on a large dataset. Because the process is slow, I want to track progress as it happens, so I include a Print[{parameter1, parameter2, ..., likelihood}] step in the function being evaluated. In doing so, I have noticed that the function appears to be evaluated twice for each trial of the parameter values. When I look at diagnostics after the fit is complete, such as the output of the EvaluationMonitor option, it shows each trial only once. For example, if Mathematica claims 20 steps after the fact, the number of printed outputs is always 40, in identical pairs. The 40 outputs appear evenly spaced in time, and the total timing of the fitting process, compared to the timing of one evaluation of the function, confirms that indeed, it was evaluated 40 times. Does anyone know why (i.e., under what conditions) FindMinimum might do this? You won't be able to evaluate my function, as it calls the datasets, but here it is anyway, with some info: lDistExp[distMaps_, e_, b1_?NumericQ] := Module[{distQ, pMaps, logList, logLike}, distQ = mapExponential2[distMaps, b1]; pMaps = Map[toProbs[#] &, distQ]; logList = Log[MapThread[#1[[#2]] &, {pMaps, e}]]; loglike=Apply[Plus, logList]; Print[{b1,logLike}]; logLike ] distMaps is a (large) matrix of reals, e is a vector of integers, and b1 is a real. The functions mapExponential2[] and toProbs[] are compiled functions (for speed). The function is maximized with respect to b1. As a side note that may be relevant, if I load the Optimization`UnconstrainedProblems` package and use the FindMinimumPlot function, the target function is be evaluated THREE times per step, even though the output again says just 20 steps. Because the fitting procedure is necessarily slow because of dataset size, I don't want to be doing more function evaluations than are necessary! Thanks, Gareth Russell Columbia University