difficulties using fmincon codes

Hello

I have follwing otimization code with function which works ith online matlab but nit in may live editor of matlabR2021a:

can someone plese help with resolution or suggesting simple combine code merging both function and program

fitting code:

clear;
a0=[1;1e-6];
options=optimset('Display','notify');  %suppress console messages unless fail to converge 
[a,sse]=fmincon(@SomnathsFunc2,a0,[],[],[],[],[],[],[],options);

%Display results
w=a(1);
t1=a(2);
fprintf('Best fit: SumSqError=%.3f, w=%.3f, t1=%.8f\n',sse,w,t1);

Best fit: SumSqError=0.020, w=1.036, t1=0.00000330

%plot results
figure;
t = [1E-7 2E-7 5E-7 1E-6 2E-6 5E-6 1E-5 2e-5 5e-5 1e-4 2e-4 5e-4 1e-3 2e-3 5e-3];
p = [0.0824 0.1515 0.2339 0.3229 0.4505 0.6173 0.7434 0.822 0.9151 0.9795 0.982 0.9829 0.9861 0.9846 0.9856];
ppred=zeros(1,length(p));
A=1;
fun=@(x,t,A,w,t1) (A*w/pi)*(1-exp(-(t/exp(x))^2))/((x-log(t1))^2+w^2);
for i=1:length(t)
    ppred(i)=integral(@(x)fun(x,t(i),A,w,t1),-Inf,Inf,'ArrayValued',1);
end
semilogx(t,p,'rx',t,ppred,'b.-');
xlabel('t');
ylabel('p(t)');
legend('Data','Fit');
grid on;

function:

function sse=SomnathsFunc2(a)
%Somnath Kale's function to be minimized, 2021-06-27
%This function written by WCR, using Somnath's data and function he provided.
%a=vector of parameters to be adjusted: a(1)=w, a(2)=t1
%v.2: Using new data and new equations, posted 6/26/2021 by Smonath Kale on
%Matlab Answers.
t = [1E-7 2E-7 5E-7 1E-6 2E-6 5E-6 1E-5 2e-5 5e-5 1e-4 2e-4 5e-4 1e-3 2e-3 5e-3];
p = [0.0824 0.1515 0.2339 0.3229 0.4505 0.6173 0.7434 0.822 0.9151 0.9795 0.982 0.9829 0.9861 0.9846 0.9856];
ppred=zeros(1,length(p));
w=a(1);
t1=a(2);
A=1;
fun=@(x,t,A,w,t1) (A*w/pi)*(1-exp(-(t/exp(x))^2))/((x-log(t1))^2+w^2);
for i=1:length(t)
    ppred(i)=integral(@(x)fun(x,t(i),A,w,t1),-Inf,Inf,'ArrayValued',1);
end
sse=sum((p-ppred).^2);
end

[Matt J]

You've omitted the error messages from your post.

[Avni Agrawal]

Hi, its working for me in both the cases. Can you share the reproduction steps if any?

[Somnath Kale]

@Matt J thank you!

plese find the error msg:

Unrecognized function or variable 'getIpOptions'.

Error in fmincon (line 859)

options = getIpOptions(options,sizes.nVar,mEq,flags.constr,defaultopt,10,0.01);

I will be beneficial if suggests a simple code without use of function. Im bit unconfertable with function uses.

[Somnath Kale]

@Avni Agrawal Im not sure then what is problem. I was thinking is it may be because my installed version of matlab which contains few products only (matlab, intrument control toolbox, signal processing tool box, and optimazation tool box only). I have attached the error msg herewith for your referance.

Answer 1

[Catalytic]

however it still uses @SomnathsFunc2 i would be happy to exclude rather than this cant we direclty add that part in code rather than calling function.

It would be silly to remove it, since it makes your code more readable. However, you can shorten the code by using lsqcurvefit instead of lsqnonlin -

clear;

t = [1E-7 2E-7 5E-7 1E-6 2E-6 5E-6 1E-5 2e-5 5e-5 1e-4 2e-4 5e-4 1e-3 2e-3 5e-3];
p = [0.0824 0.1515 0.2339 0.3229 0.4505 0.6173 0.7434 0.822 0.9151 0.9795 0.982 0.9829 0.9861 0.9846 0.9856];


% Define initial guess for parameters
a0 = [1; 5e-5];

% Define options for lsqnonlin
options = optimoptions('lsqcurvefit','Display','final');

% Perform optimization using lsqnonlin
a = lsqcurvefit(@SomnathsFunc2,a0,t,p,[],[],options);

Local minimum possible.

lsqcurvefit stopped because the final change in the sum of squares relative to 
its initial value is less than the value of the function tolerance.

% Display results
w = a(1);
t1 = a(2);
fprintf('Best fit: w=%.3f, t1=%.8f\n', w, t1);

Best fit: w=1.036, t1=0.00000330

% Plot results
semilogx(t, SomnathsFunc2(a,t),'b.-',t,p,'xr');
xlabel('t'); ylabel('p(t)'); legend('Data', 'Fit'); grid on;

function ppred = SomnathsFunc2(a,t)

   ppred = zeros(1, length(t));
    w = a(1);
    t1 = a(2);
    A = 1;
    fun = @(x,t,A,w,t1) (A*w/pi)*(1-exp(-(t/exp(x)).^2))./((x-log(t1)).^2+w^2);
    for i = 1:length(t)
        ppred(i) = integral(@(x)fun(x,t(i),A,w,t1),-Inf,Inf,'ArrayValued',1);
    end

end

Answer 2

[Avni Agrawal]

Hi Somnath,

I understand that you're encountering an error related to the `fmincon` function. To address this issue effectively, it's essential to confirm whether the Optimization Toolbox is installed on your machine.

You can verify the presence of the Optimization Toolbox by following these steps:

1. Check for the existence of the file 'getIpOptions.m' in the directory specified below:

winopen(fullfile(matlabroot,'toolbox\optim\optim'))

This command should open the directory where the function is stored. Look for the 'getIpOptions.m' file in that directory.

2. If the file exists, but the problem persists, it's possible that the path to the file has been somehow removed. Restart MATLAB and see if the issue resolves. Additionally, check your 'startup.m' file (if it exists) to ensure that important paths are not being removed. You can also try running `restoredefaultpath`.

3. If the 'getIpOptions.m' file does not exist in the specified directory, it indicates that the Optimization Toolbox may not be installed on your system. In such a scenario, consider reinstalling the Optimization Toolbox to resolve the issue.

I hope this helps.

[Somnath Kale]

@Avni Agrawal Thank You! There was problem with optimazaion tool boox however Im still not fomfertale with code mentoined above. the t and p values mentined above in the function are essentially the variable and not fixed array. when i tried ro assign variable values to them it encountered following error:

I have tried

t=X;

p=Y;

Unrecognized function or variable 'X'.

Error in SomnathsFunc2 (line 7)

t = X

Error in fmincon (line 567)

initVals.f = feval(funfcn{3},X,varargin{:});

Caused by:

Failure in initial objective function evaluation. FMINCON cannot continue.

How can i take care of this. Plese suggest if any altrenate code this (without use of function)

[Avni Agrawal]

What is X over here? Is it defined? Have you tried re-installing optimization toolbox?

[Avni Agrawal]

If you want to find the best fit parameters without using `fmincon`, you can directly minimize the sum of squared errors (SSE) using other optimization methods or techniques. One common approach is to use MATLAB's built-in optimization functions such as `lsqnonlin`, which is commonly used for nonlinear least squares optimization.

Here's how you can modify the code to use `lsqnonlin`:

clear;

% Define initial guess for parameters
a0 = [1; 5e-5];

% Define options for lsqnonlin
options = optimoptions('lsqnonlin','Display','iter');

% Perform optimization using lsqnonlin
a = lsqnonlin(@SomnathsFunc2,a0,[],[],options);

Warning: Trust-region-reflective algorithm requires at least as many equations as variables; using Levenberg-Marquardt algorithm instead.

                                        First-order                     Norm of 
 Iteration  Func-count      Resnorm      optimality       Lambda           step
     0           3          1.31419        1.75e+04         0.01
     1          17         0.813953        1.75e+04        1e+09    1.42146e-05
     2          20         0.382598         1.6e+04        1e+08    1.27183e-05
     3          23       0.00208238        2.56e+03        1e+07    2.08443e-05
     4          26      0.000476598             189        1e+06    8.12187e-07

Local minimum possible.
lsqnonlin stopped because the relative size of the current step is less than
the value of the step size tolerance.

% Display results
w = a(1);
t1 = a(2);
fprintf('Best fit: w=%.3f, t1=%.8f\n', w, t1);

Best fit: w=1.000, t1=0.00000303

% Plot results
figure;
t = [1E-7 2E-7 5E-7 1E-6 2E-6 5E-6 1E-5 2e-5 5e-5 1e-4 2e-4 5e-4 1e-3 2e-3 5e-3];
p = [0.0824 0.1515 0.2339 0.3229 0.4505 0.6173 0.7434 0.822 0.9151 0.9795 0.982 0.9829 0.9861 0.9846 0.9856];
ppred = zeros(1, length(p));
A = 1;
fun = @(x,t,A,w,t1) (A*w/pi)*(1-exp(-(t/exp(x)).^2))./((x-log(t1)).^2+w^2);
for i = 1:length(t)
    ppred(i) = integral(@(x)fun(x,t(i),A,w,t1),-Inf,Inf,'ArrayValued',1);
end
semilogx(t, p, 'rx', t, ppred, 'b.-');
xlabel('t');
ylabel('p(t)');
legend('Data', 'Fit');
grid on;

function sse = SomnathsFunc2(a)
% Somnath Kale's function to be minimized, 2021-06-27
% This function written by WCR, using Somnath's data and function he provided.
% a = vector of parameters to be adjusted: a(1) = w, a(2) = t1
% v.2: Using new data and new equations, posted 6/26/2021 by Somnath Kale on MATLAB Answers.

t = [1E-7 2E-7 5E-7 1E-6 2E-6 5E-6 1E-5 2e-5 5e-5 1e-4 2e-4 5e-4 1e-3 2e-3 5e-3];
p = [0.0824 0.1515 0.2339 0.3229 0.4505 0.6173 0.7434 0.822 0.9151 0.9795 0.982 0.9829 0.9861 0.9846 0.9856];
ppred = zeros(1, length(p));
w = a(1);
t1 = a(2);
A = 1;
fun = @(x,t,A,w,t1) (A*w/pi)*(1-exp(-(t/exp(x)).^2))./((x-log(t1)).^2+w^2);
for i = 1:length(t)
    ppred(i) = integral(@(x)fun(x,t(i),A,w,t1),-Inf,Inf,'ArrayValued',1);
end
sse = sum((p-ppred).^2);
end

In this code, `lsqnonlin` is used to minimize the sum of squared errors directly, without the need for a constrained optimization approach. The optimization is performed by adjusting the parameters `w` and `t1` to minimize the difference between the predicted and observed values of `p`.

[Somnath Kale]

@Avni Agrawal thank you for your suggested code using lsnonlin function. however it still uses @SomnathsFunc2 i would be happy to exclude rather than this cant we direclty add that part in code rather than calling function. Unfortunatelt that involvemnt of integration is making it bit ununderstandale to me.

Plese suggets if possible!

I apreciate your time and efforts!

Answer 3

[Somnath Kale]

@Avni Agrawal and @Catalytic thanks for your sugestions. both of your answers were realy helpful. But unfortunately matlab dose not allow to accept both the answers. I can accept only one.

[Matt J]

But you can upvote any answer, even ones that you didn't accept, as I have done for @Avni Agrawal just now.

[Somnath Kale]

Thank you @Matt J.! I Just did it.