fminsearch terminates/converges for a high fval

Hello, I am trying to estimate the parameters of a function but the optimization terminates even though the objective function is high.

I show below two cases, the first case is OK to me, the second case is where I have the problem.

In 1) you can see that min f(x) is 6.28017e-30, the value of the objective function is low enough.

However, in case 2) optimization terminates but the value of the objective function is 0.9391 which is still very high.

How can I make the optimization continue until it meets the criteria (when "fval" is low enough) ? Thanks

options = optimset('Display', 'iter', 'MaxFunEvals', 1e8, 'MaxIter', 1e6, 'TolX', 1e-10, 'TolFun', 1e-14);
[params fval] = fminsearch(@(B) fun(B,...), inival, options);

1) OK CASE (final fval low enough)

   Iteration   Func-count     min f(x)         Procedure
       0            1         0.035832         
       1            4         0.035832         initial simplex
       2            6       0.00525569         expand
  ...
     526          927       2.1518e-29         contract outside
     527          929      6.28017e-30         contract inside

Optimization terminated:
 the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-10 
 and F(X) satisfies the convergence criteria using OPTIONS.TolFun of 1.000000e-14 

fval =

     6.2802e-30

2) BAD CASE (final fval very high)

Iteration   Func-count     min f(x)         Procedure
     0            1         0.940907         
     1            4         0.939127         initial simplex
     2            9         0.939127         shrink
...
    48          239         0.939127         shrink
    49          241         0.939127         contract outside

Optimization terminated:
 the current x satisfies the termination criteria using OPTIONS.TolX of 1.000000e-10 
 and F(X) satisfies the convergence criteria using OPTIONS.TolFun of 1.000000e-14 

fval =

      0.9391

Answer 1

[Matt J]

The final value of the objective function is not a good indicator of whether the solver has succeeded. For example, you could repeat case 2 with fun() simply translated downward

[params fval] = fminsearch(@(B) fun(B,...)-0.939127, inival, options);

You will get the same solution for "params", but a much smaller value for fval.

It is possible, of course, that you simply got stuck in a local minimum. If that's what happened, making the solver continue iterating will not help. You need a better initial guess, inival.