Matlab coding errors call when run..Please help to solve this problem

% Define the initial point x0 and the size reduction parameter 
Delta x0 = [1 1]; 
Delta = [2 2];
% Set the tolerance epsilon 
epsilon = 0.001;
% Initialize the current best point x_bar to x0
x_bar = x0;
% Set the maximum number of iterations
max_iter = 1000;
% Initialize the iteration counter
iter = 0;
% Start the optimization loop
while iter < max_iter 
    % Check if the norm of Delta is greater than the tolerance
    if norm(Delta) <= epsilon
        % Return x_bar as the optimal solution 
        break; 
    end
    % Create a hypercube of 20 points around x_bar by adding and subtracting Delta
    x1 = x_bar - Delta;
    x2 = x_bar + Delta;
    hypercube = combvec(x1, x2)

Answer 1

[Tejas]

Hello @FAKHRULRAZI,

Here is an example that shows, how the above mentioned optimization problem can be coded:

• Begin by defining the objective function. Below is a sample objective function. For more details on how to define a function, refer to this documentation: https://www.mathworks.com/help/releases/R2022b/matlab/ref/function.html

    function f = objective_function(x)
        f = sum(x.^2);
    end 

• Inside the iteration loop, include the code snippet below to exit the loop once the optimal value is found.

    if norm(Delta) <= epsilon
        disp('Optimal solution found');
        disp(x_bar);
        break;
    end 

• Create a hypercube according to the requirements.

    x1 = x_bar - Delta;
    x2 = x_bar + Delta;
    hypercube = combvec(x1, x2)'; 

• Use the code snippet provided below to identify the point in the hypercube with the minimum value of the objective function. Below code snippet uses 'Function Handle' to evaluate objective function at each point of hypercube. For more information on function handles, refer to this documentation: https://www.mathworks.com/help/releases/R2022b/matlab/matlab_prog/creating-a-function-handle.html

    f_values = arrayfun(@(i) objective_function(hypercube(i, :)), 1:size(hypercube, 1));
    [~, min_index] = min(f_values);
    x_bar = hypercube(min_index, :); 

• Increment the iterator value.

    Delta = Delta * 0.5;
    iter = iter + 1;

Answer 2

[Walter Roberson]

You are missing incrementing iter inside the while loop.

Your while loop is missing an end statement.

You are not changing Delta or epsilon in your while loop, so the if norm(Delta) <= epsilon will either always be true or always be false, so you might as well pull the test outside of the while loop.

You are not doing anything with hypercube so the end result for hypercube will be whatever it was assigned in the last iteration. In such a situation you might as well only do the last iteration.