Find the x value from a specific iteration of fmincon

How can I extract the the value of x at the iteration 5 when f(x)= 0.300877 after the optimization procedure.

                                  Max   Line search  Directional First-order 
  Iter F-count        f(x)   constraint steplength   derivative  optimality Procedure 
     0      3            1           -1                                         
     1      9     0.953127      -0.9375      0.125         -2       12.5   
     2     16     0.808446      -0.8601     0.0625      -2.41       12.4   
     3     21     0.462347       -0.836       0.25      -12.5       5.15   
     4     24     0.340677      -0.7969          1      -4.07      0.811   
     5     27     0.300877      -0.7193          1     -0.912       3.72   
     6     30     0.261949      -0.6783          1      -1.07       3.02   
     7     33     0.164971      -0.4972          1     -0.908       2.29   
     8     36     0.110766      -0.3427          1     -0.833          2

Answer 1

[Massimo Zanetti]

From the help page about Output Functions Output Functions you can extract this way to save iterates of the solver. Assume you want to minimize the function f(x1,x2) = 4*x1^2 + 2*x2^2, then:

1. Define your problem by nesting functions into one main function:

function [x fval history] = myproblem(x0)
    history = [];
    options = optimset('OutputFcn', @myoutput);
    [x fval] = fminsearch(@objfun, x0,options);

      function stop = myoutput(x,optimvalues,state);
          stop = false;
          if isequal(state,'iter')
            history = [history; x];
          end
      end

      function z = objfun(x)
        z = 4*x(1)^2+2*x(2)^2;
      end
  end

1. Trigger the solver (with one starting value x0) and retrieve all iterates the solver has computed in the matrix history

x0 = [1,2];
[x,val,history] = myproblem(x0);

Inspect matrix history, each row is the k-th iterate. The same procedure works for fmincon.