Calling function in fminsearch

I want to call a function lamda to update initial value in fminsearch.

The initial value of lambda(1) =-1.

I want to update in lambda as lambda(i+1)=lambda(i)-0.01*(lambda(end)).

This computation of lambda should continue until lambda(end) < 0.01. I am not able to call function in fminsearch as FMINSEARCH accepts inputs only of data type double.

close all
clear all
clc

[optimal_lambda,cost] = fminsearch(@cost_lambda, @lamda)
a = optimal_lambda(1)

function cost = cost_lambda(lambda)
   part_a = @(t,y)[-0.02*y(1); (y(2)/0.8)*(1/0.8)*exp(0.01*t)];
   [t,y]=ode45(part_a, [0 10], [0.5,-1]');
   cost = (1-(1/0.01)*(1-exp(-log((-1+(y(1)/0.8)^2)/(0.015*lambda(1)*exp(0.01*t)))))*(1-(y(1)/0.8))^2);
   
function lambda = lamda(lambda)
    lambda(1)=-1;
    i=1;
        for lambda(end)<0.01

Invalid expression. When calling a function or indexing a variable, use parentheses. Otherwise, check for mismatched delimiters.

Error in connector.internal.fevalMatlab

Error in connector.internal.fevalJSON

    lambda(i+1)=lambda(i)-0.01*lambda(end)
    i=i++
        end
end
end

[Torsten]

Unclear.

[Yokuna]

Thanks. Updated.

[Torsten]

What is the function "lamda" for ? "fminsearch" searches for a value of "lambda" such that the objective function becomes minimal. There is no reason to vary or prescribe lambda on your own. fminsearch will do this for you.

Answer 1

[Steven Lord]

If you mean you want to call fminsearch repeatedly with different initial points, call it in a loop.

f = @sin;
initialPoints = (0:0.5:10).';
solutions = zeros(size(initialPoints));
for k = 1:numel(initialPoints)
    x0 = initialPoints(k);
    solutions(k) = fminsearch(f, x0);
end

For ease of display I'll put the points in a table.

results = table(initialPoints, solutions)

results = 21×2 table
    initialPoints    solutions
    _____________    _________

           0          -1.5708 
         0.5          -1.5708 
           1          -1.5708 
         1.5          -1.5708 
           2           4.7124 
         2.5           4.7124 
           3           4.7124 
         3.5           4.7124 
           4           4.7124 
         4.5           4.7124 
           5           4.7124 
         5.5           4.7124 
           6           4.7124 
         6.5           4.7124 
           7           4.7124 
         7.5           4.7124 

[Yokuna]

Thanks! But I need the initial value as the value obtained in previous iteration of solution.

So initialPoints are not predefined but calculated in each iteration.

[Steven Lord]

Okay. I'll use randi to compute my initial points, but you could use another function. In fact you could (except when whichTrial is 1) look at results(whichTrial-1) to use the results from the previous run as x0 for this run.

ntrials = 10;
initialPoints = zeros(ntrials, 1);
results = zeros(ntrials, 1);
f = @sin;
for whichTrial = 1:ntrials
    x0 = randi([-10 10]); % You could compute this however you want
    initialPoints(whichTrial) = x0; % Record it
    results(whichTrial) = fminsearch(f, x0); % Compute with it
end

Now show the results table.

t = table(initialPoints, results)

t = 10×2 table
    initialPoints    results
    _____________    _______

         -5           -7.854
         -8           -7.854
          2           4.7124
         -6           -7.854
         10           10.996
         10           10.996
          9           10.996
          1          -1.5708
         10           10.996
         -3          -1.5708