FindFit with constraints is slow

*To*: mathgroup at smc.vnet.net*Subject*: [mg89207] FindFit with constraints is slow*From*: Matt.Latourette at rad.msu.edu*Date*: Thu, 29 May 2008 07:04:49 -0400 (EDT)

I'm using FindFit to fit the parameters of an exponential decay. I'd like to include constraints to force the output parameters to be non- negative since negative values do not make any sense in the real world situation being modeled. The FindFit operation occurs within a function that is called many times. However, when I do this the total computation time increases drastically (by 3 orders of magnitude). Any thoughts on why the version with constraints is so incredibly slow? The original code: FindFit[OrderedPairList, \ Global`M0*Exp[-Global`R2Star*t], {{Global`M0, initM0}, \ {Global`R2Star, initR2Star}}, {t}, MaxIterations->500, \ Method->Automatic, \ AccuracyGoal->3, PrecisionGoal->3, \ WorkingPrecision->MachinePrecision] The code with constraints: FindFit[OrderedPairList, \ {Global`M0*Exp[-Global`R2Star*t], Global`R2Star>=0, \ Global`M0>=0}, \ {{Global`M0, initM0}, {Global`R2Star, initR2Star}}, \ {t}, MaxIterations->500, Method->Automatic, \ AccuracyGoal->3, PrecisionGoal->3, \ WorkingPrecision->MachinePrecision] where OrderedPairList represents data of the form {{x1, y1}, {x2, y2}, ... {xn, yn}} where the x's and y's are floats and initM0 and initR2Star are real-valued constants.