Problem with lsqnonlin: Optimization completed because the size of the gradient at the initial point is less than 1e-4 times the value of the function tolerance.

Hi,

I have a function "fun103r" and it's output is "ER". I am transforming this function to an optimization expression using "fcn2optimexpr" to optimize "ER" with a coouple of variables including "k". The optimization variable is k (8x1). And to define extra (non-optimized) parameters, I'm using an anonymus function "f". Unfortunately, no iteration is performed when I try to use "lsqnonlin" and I receive this message: "Optimization completed because the size of the gradient at the initial point is less than 1e-4 times the value of the function tolerance".

I'll be glad if you could help.

clear; 
clc;
%run('Fun103r');
Pa =216;      
sp=7;
L=0.2; 
Lb=[13.2 14.0 14.0 14.0 14.0 14.0 13.2]; 
N=zeros(sp); 
ss=0;
E = 3.4342e10;   
J = 0.9028 ;
na=6; 
d1=[2.0 4.0 6.2 15.2 17.4 19.4];  
opts = detectImportOptions('AppBR.xlsx'); 

Error using detectImportOptions
Unable to find or open 'AppBR.xlsx'. Check the path and filename or file permissions.

preview('AppBR.xlsx',opts);
opts.Sheet = 'D1-3BR';
opts.SelectedVariableNames = [1:9]; 
opts.DataRange = '2:484';
Rtr3=readmatrix('AppBR.xlsx',opts);  
k = optimvar('k',8,1); % 8-by-1 optimization variable
[ER] = fcn2optimexpr(@Fun103r,k); % transformation of function "Fun103r"  
k0=[100000; 200000; 100000; 200000; 200000; 100000; 200000; 100000]; % starting point for k
f = @(k)Fun103r(ss,Pa,sp,L,Lb,N,E,J,na,d1,k,Rtr3); % anonymus function to consider extra (non-optimized) parameters
options = optimoptions('lsqnonlin','Display','iter','FiniteDifferenceStepSize',1e-3); 
options.StepTolerance = 1e-10;
options.Algorithm = 'levenberg-marquardt';
k=lsqnonlin(f,k0,options);

[Matt J]

No, we cannot help because we cannot see Fun103r. However, there is no reason to think a priori that anything is wrong. If, for example, f(k)=0 for all k, obviously any intial point you select will be optimal and there is no need to keep iterating.

[Sinem Tola]

Hi, I've attached the code here. Actually, not all values of k makes ER (routput of Fun103r) zero. I can't undestand why there are no iterations.

[Torsten]

It's necessary that the functions ER you return to lsqnonlin from "Fun103r" are differentiable with respect to the parameters k. If statements and round commands are forbidden. So there is no hope you will get reasonable results for k.

Did you call Fun103r with your initial values for k and inspected the results returned from your function ?

[Sinem Tola]

Thank you, you are right. I've forgotten about the supported operations. That's why the nested function doesn't work either to pass extra parameters..And yes I've run Fun103r for far values and yes the error gets bigger. Then, it seems there's no optimizaiton solution using MATLAB.