How to visualize the iterations of an optimization problem ?

Hi everybody,

I recently started to learn how to optimize a continuous function and I want to get a figure like the one I attached as one of the outputs but I do not know how to code that.

prob = optimproblem
%defining variables
x= optimvar('x',"LowerBound",-2.5,'UpperBound',2.5);
y= optimvar('y',"LowerBound",-2.5,'UpperBound',2.5);
%ndefining objective function
prob.Objective=log(1+3.*(y-(x.^3-3)).^2+(x-4/3).^2);
%setting initial guess
initialpt.x=-1
initialpt.y=2
%options
options=optimoptions(prob,'Display','iter')
[sol,fval,exitflag,output]=solve(prob,initialpt,'options',options);
disp("# of function evaluations:"+output.funcCount)
fval
sol
exitflag

I want to have the following figure as an output:

Thank you

Answer 1

[Matt J]

function main

   xhist=[];

    prob = optimproblem
    %defining variables
    x= optimvar('x',"LowerBound",-2.5,'UpperBound',2.5);
    y= optimvar('y',"LowerBound",-2.5,'UpperBound',2.5);
    %ndefining objective function
    prob.Objective=log(1+3.*(y-(x.^3-3)).^2+(x-4/3).^2);
 
    %setting initial guess
    initialpt.x=-1;
    initialpt.y=2;
    %options
    options=optimoptions(prob,'Display','iter','OutputFcn',@histfunc);
    [sol,fval,exitflag,output]=solve(prob,initialpt,'options',options);

    
        fcontour( @(x,y)  log(1+3.*(y-(x.^3-3)).^2+(x-4/3).^2));
        hold on
        plot(xhist(1,:), xhist(2,:),'-om','MarkerFaceColor','b');
        hold off
 

    function stop = histfunc(x,optimValues,state)
    
        stop = 0;
        
        if state~="iter"; return; end
        
        xhist=[xhist,x(:)];
 
    end

end

[Mohammad Assar]

Thank you, it was a lot of help.