Is there a way to plot the output of my function for fmincon evaluations?

I want to plot the progression of my objective as it is being optimized by fmincon. I was hoping the output would be in a regular pattern (for my three variable function, something like: 1. del_x_step, 2. del_y_step, 3. del_z_step, [evaluate gradient, etc], 4. new position) so I could just plot every 4th step. However upon viewing the outputs, I see that the function seems to bounce around a bit between successive iterations.

                                                          Norm of First-order
 Iter F-count            f(x) Feasibility  Steplength        step  optimality
    0       4   -1.848033e+04   3.097e+01                           8.456e+01
    1       9   -2.084884e+04   0.000e+00   7.000e-01   6.711e+01   3.159e+02
    2      22   -2.086112e+04   0.000e+00   4.035e-02   2.496e+00   3.015e+02
    3      26   -2.227361e+04   0.000e+00   1.000e+00   1.393e+01   1.816e+02
    4      37   -2.228014e+04   0.000e+00   8.235e-02   2.194e+00   7.227e+01
    5      41   -2.243568e+04   0.000e+00   1.000e+00   1.467e+00   2.271e+02
    6      47   -2.270094e+04   0.000e+00   4.900e-01   9.539e+00   8.021e+01
    7      51   -2.271830e+04   0.000e+00   1.000e+00   3.290e+00   1.466e+02
    8      60   -2.272500e+04   0.000e+00   1.681e-01   1.128e+00   1.370e+02
    9      91   -2.273291e+04   0.000e+00   6.571e-05   1.702e+00   7.642e+01
   10      95   -2.276594e+04   0.000e+00   1.000e+00   2.046e+00   1.681e+02
   11     120   -2.276670e+04   0.000e+00   5.585e-04   6.198e-04   1.664e+02
   12     126   -2.276754e+04   0.000e+00   4.900e-01   3.616e-02   1.656e+02
   13     148   -2.276926e+04   0.000e+00   1.628e-03   3.320e-04   1.684e+02
   14     175   -2.276926e+04   0.000e+00   6.571e-05   3.230e-05   1.684e+02

Optimization stopped because the relative changes in all elements of x are
less than options.TolX = 1.000000e-06, and the relative maximum constraint
violation, 0.000000e+00, is less than options.TolCon = 1.000000e-06.

Optimization Metric                                         Options
max(abs(delta_x./x)) =   7.75e-07                    TolX =   1e-06 (default)
relative max(constraint violation) =   0.00e+00    TolCon =   1e-06 (default)

My questions are:

1. Is there a straightforward explanation for the additional function evaluations adding to the f-count? 2. Is it reasonable to just plot the output at each iteration (e.g. at 4, 9, 22, etc shown above)?

Answer 1

[Alan Weiss]

It is not clear that you are obtaining a true minimum. See the documented suggestions on what to do to ensure that you have a real minimum.

As for plotting, have you tried to use one of the built-in plot functions? Perhaps @optimplotfval would give you what you seek.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation

[Cy]

Yes, I was also going to ask about that first-order optimality condition. Thanks for the help. The built-in functions work just fine. Somehow I missed that.