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FindMinimum returning different results when used inside a function

Posted 11 years ago
I am trying to fit some data by minimizing a function of four parameters. However, this function appears to have a bunch of local minima. To mitigate this, I wrote a function that forms a grid and systematically moves to the minimum until the minimum is at the center of the grid (this is a very inefficient method of grid searching, but simple). I then plug the values found by the grid into FindMinimum as starting values. Unfortunately, FindMinimum returns to the original point, even though this point is definitely higher than the one I found. The frustrating thing about this is that if I manually copy the parameter values found by the grid search into FindMinimum as start values, it finds a completely different, much lower point (even though all the options are the same). Anyone know why this is happening? Here is the code:
 Clear[detailedsearch];
 detailedsearch[i_, rstart_: 1.4*10^-5, Rstart_: 12*10^-5, Crstart_: 0,
     CRstart_: 0, rdelta_: .01*10^-5, Rdelta_: .5*10^-5, Crdelta_: .1,
    CRdelta_: .1, klist_: Range[50]] :=
  
   Module[{r, rold, R, Rold, Cr, Crold, CR, CRold, set, block, out,
     index, x, y, z, w},
    rold = rstart; Rold = Rstart; Crold = Crstart; CRold = CRstart;
    Print[{rold, Rold, Crold, CRold}];
   set = FindMinimum[\[Chi]o[i, rp, Crp, klist] + \[Chi][i, rp, Rp,
       Crp, klist], {rp, rold}, {Rp, Rold}, {Crp, Crold}, {CRp, CRold},
     MaxIterations -> 10000, Method -> "Newton"];
   {rold, Rold, Crold, CRold} = Table[set[[2]][[j, 2]], {j, 4}];
   set = FindMinimum[\[Chi]o[i, rp, Crp, klist] + \[Chi][i, rp, Rp,
       Crp, klist], {rp, rold}, {Rp, Rold}, {Crp, Crold}, {CRp, CRold},
     MaxIterations -> 10000, AccuracyGoal -> 8, Method -> "Newton"];
   {rold, Rold, Crold, CRold} = Table[set[[2]][[j, 2]], {j, 4}];
   Print[{rold, Rold, Crold, CRold}];
   While[True,
    block =
     Table[\[Chi][i, rold + rdelta*x, Rold + Rdelta*y,
        CRold + CRdelta*w, klist] + \[Chi]o[i, rold + rdelta*x,
        Crold + Crdelta*z, klist],
      {x, -1, 1}, {y, -1, 1}, {z, -1, 1}, {w, -1, 1}];
    Print[Min[block]];
    index = Position[block, _?(# == Min[block] &)];
    Print[index];
    If[index == {{2, 2, 2, 2}},
     Break[],
     {
      {{x, y, z, w}} = index - {{2, 2, 2, 2}};
      Print[{x, y, z, w}];
      rold += x*rdelta; Rold += y*Rdelta; Crold += z*Crdelta;
      CRold += w*CRdelta;
     
      }];
    ];
   Print[{rold, Rold, Crold, CRold}];
   set = FindMinimum[\[Chi]o[i, rp, Crp] + \[Chi][i, rp, Rp,
       Crp], {rp, rold}, {Rp, Rold}, {Crp, Crold}, {CRp, CRold},
     MaxIterations -> 10000, AccuracyGoal -> 8, Method -> "Newton",
     PrecisionGoal -> 8];
   {rold, Rold, Crold, CRold} = Table[set[[2]][[j, 2]], {j, 4}];
   {rold, Rold, Crold, CRold}
   ];
POSTED BY: Joshua Dempster
Suggest you try NMinimize;  It is the numeric global minimization function. 
POSTED BY: Frank Kampas
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