problem finding minimum of residual for separable nonlinear least square using fminsearch

Dear All, I have some ultrasonic signal that I created wavelet transform for. I am trying to do separable nonlinear least square between measured signal(function of time and frequency) and reference model. to get the maximization criterion I made derivation for different equations and reshaping of the matrix to be a vector instead of a matrix in order to match fminsearch. Please find attached for the equations required to perform for the maximization criterion the final model I needed to maximize is shown below:

I tried to use fminsearch function to get the minimum value of t_center but I can not get any solution. it says: Exiting: Maximum number of function evaluations has been exceeded - increase MaxFunEvals option. I already increased MaxFunEvals and MaxIter to 1000 but still not possible. Please find below the code I made and tell me what is wrong with it. I already attached the m-file for better reading of the code.

function max_criterion = myfun(t_center)
global F s  
w=2*pi*F';
t=linspace(0,0.015,3000);      
w_center=2*pi*200000; 
w1=2*pi;   
eeta=w./w1;  
Y=s;    
B=100000; 
A=1/2.*sqrt((2.*eeta)./(pi.*(B^2+4.*eeta.^2)).*exp(-2.*(w-w_center).^2./(B.^2+4.*eeta.^2)));  
k= -B.^2.*eeta.^2./(2.*(B.^2+4.*eeta.^2))*(t-t_center).^2; 
kai= ((4*w_center*eeta.^2)./(B^2+4.*eeta.^2)+B^2.*w./(B^2+4.*eeta.^2))*(t_center-t);   
Z=repmat(A,1,length(t));
H=Z.*exp(k).*exp(1i.*kai);    
H_new=(reshape(H,numel(H),1));   
Y_new=(reshape(Y,numel(Y),1));   
max_criterion= -1000000000.*Y_new'*H_new*((H_new'*H_new)\H_new')*Y_new; 
end

then I am trying to use fminsearch function to extract the local minimum but it never give a solution:

options=optimset('tolx',1e-18,'tolfun',1e-18,'MaxFunEvals',1000,'MaxIter',1000);
 t_center_ini =  0.000591;
[t_center,fval,exitflag,output] = fminsearch(@myfun,t_center_ini,options)

I tried to use function "fminbnd" and it gave results but I am afraid to use because it works only with continuous functions and may be the wavelet transform have discontinuities.

Can you please help me with that. what is the mistake I do. Best Regards, Hossam Selim

Answer 1

[Alan Weiss]

1. fminbnd is not just for continuous functions. It should converge to something reasonable if you give it an initial interval where the function is not NaN or Inf or complex.
2. Please format your code using the {} Code button so we can read it.
3. Even better, try explaining what you are trying to do in words.

Just my suggestions,

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[John D'Errico]

I'm not going to go through your code. HOWEVER, I will point out that I've already written a separable least squares solution that is based on fminsearch. It is on the file exchange, called fminspleas.

Having said that, I also don't know how many nonlinear unknowns you are solving for using these tools. I tend to suggest an upper limit of 6 to at most 8 unknowns. Beyond that point is usually just a waste of CPU time with fminsearch. It may explain why you are having problems though.

Answer 3

[Hossam Selim]

Thanks a lot for ur fedback. I am having only one nonlinear unknown. I will use your code and I hope it solves my issue I choose different initial conditions with same problem best regards Hossam