Problem of NUMERICAL constraints (Ndsolve) with Nminimize

*To*: mathgroup at smc.vnet.net*Subject*: [mg100759] Problem of NUMERICAL constraints (Ndsolve) with Nminimize*From*: Anh Ngoc LAI <laianhngoc at yahoo.com>*Date*: Sat, 13 Jun 2009 06:02:42 -0400 (EDT)

Hello everybody, I have to optimize an function with numerical constraints using Nminimize. To construct the constraints, i have to solve a system of ODEs (type): Sol=NDSolve[{{B'[ t] == -(t6 + t13) B[t] -(t7 + t15 + t14*t11) F[ t] +(1/2)*(B[t] B[t] + t11*F[t] F[t] + t12*GG[t] GG[t]) - t2, F'[t] == -t8*F[t] - t3, GG'[t] == -(t9 + t16) F[t] - (t10 + t17) GG[t] - t4, A'[t] == t5 B[t] +((t5*t7/t6) - t14) F[ t] +(1/2)*(F[t] F[t] + GG[t] GG[t]) - t1}, {B[0] == F[0] == GG[0] == A[0] == 0}}, {B, F, GG, A}, {t, 0, 10}][[1]] where t1,...,t17 are parameters to obtain. and then i have to use A,B,F,GG and my data to construct this constraints. So i use WITH (or Block) commend for it: f[t1_?NumericQ, t2_?NumericQ, t3_?NumericQ, t4_?NumericQ, t5_?NumericQ, t6_?NumericQ, t7_?NumericQ, t8_?NumericQ, t9_?NumericQ, t10_?NumericQ, t11_?NumericQ, t12_?NumericQ, t13_?NumericQ, t14_?NumericQ, t15_?NumericQ, t16_?NumericQ, t17_?NumericQ] := With[{...}, C] Here C are constraints to put on Nminimize optimization. I don't know how to deal with this, if C is only one constraint i have no problem with, but here C is a list. For Mathematica, f1[t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14, t15, t16, t17] is only one element and not a List. I think to another way to solve this problem which is to get A,B,F,GG by defining functions directly with Ndsolve (then construct constraints with Data without using WITH) but i have to evaluate a lot of time NDSOLVE on my procedure, and it take a much of time. That will be great if someone could give an idea. Thanks.