NMinimize/FindMinimum and function involving NDSolve

*To*: mathgroup at smc.vnet.net*Subject*: [mg46219] NMinimize/FindMinimum and function involving NDSolve*From*: kzhang at flashmail.com (Kezhao Zhang)*Date*: Thu, 12 Feb 2004 07:15:46 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello, I tried to find the initial condition for a second order ODE by numerically solving the equation and using NMinize or FindMininum. The objective to be minimized is defined as a function of c1 and c2, the initial condition. The problem is that NMimize and FindMinum complain that NDSolve::"ndinnt": "Initial condition x is not a number or a rectangular array of numbers". I wonder if NMinimize and FindMinimum can take a function involving complex rpocedurals like NDSolve. If not, is there a workaround? My code is listed below. Thanks for your help. In[]:=objective[c1_, c2_] := Module[{x, t, s, xx}, xx = Linspace[0, 2., 40]; s = NDSolve[{x''[t] - x'[t] + x[t] == 0, x[0] == c1, x'[0] == c2}, x, {t, 0, 2}]; Total[(First[x /. s][#] - Exp[#/2] Cos[Sqrt[3]/2#])^2 & /@ xx]] In[]:=FindMinimum[objective[x, y], {{x, 1}, {y, 1}}] or In[]:=NMinimize[objective[x, y], {x, y}] gives error message "NDSolve::ndinnt: Initial condition x is not a number or a rectangular array of numbers." K. Zhang

**Follow-Ups**:**Re: NMinimize/FindMinimum and function involving NDSolve***From:*Daniel Lichtblau <danl@wolfram.com>