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;
