Fminunc. First order optimality not close to zero.

The results from my code are:

%options = optimset(options, 'TolCon',1e-10);

%options = optimset(options, 'TolFun',1e-10);

%options = optimset(options, 'TolX',1e-10);

 Diagnostic Information

Number of variables: 3

Functions Objective and gradient: ola_2unc/Lik Hessian: finite-differencing (or Quasi-Newton)

Algorithm selected large-scale: trust-region Newton

__________________________________________________________ End diagnostic information

                                Norm of      First-order 
 Iteration        f(x)          step          optimality   CG-iterations
     0              22602                           420                
     1            22601.1      0.0575789           29.4           1
     2            22601.1      0.0258237           29.4           1
     3            22601.1     0.00645593           29.4           0
     4            22601.1     0.00161398           29.4           0
     5            22601.1    0.000403496           29.4           0
     6            22601.1    0.000100874           29.4           0
     7            22601.1    2.52185e-05           29.4           0
     8            22601.1    6.30462e-06           29.4           0
     9            22601.1    1.57616e-06           29.4           0
    10            22601.1    3.94039e-07           29.4           0
    11            22601.1    9.85097e-08           29.4           0
    12            22601.1    2.46274e-08           29.4           0
    13            22601.1    6.15686e-09           29.4           0
    14            22601.1    1.53921e-09           29.4           0
    15            22601.1    3.84803e-10           29.4           0
    16            22601.1    9.62009e-11           29.4           0

Local minimum possible.

fminunc stopped because the size of the current step is less than the selected value of the step size tolerance.

criteria details

Elapsed time is 1072.305964 seconds.

exitflag =

     2

output =

         iterations: 16
          funcCount: 17
       cgiterations: 2
      firstorderopt: 29.3953
          algorithm: 'large-scale: trust-region Newton'
            message: [1x419 char]
    constrviolation: []

I would like to ask:

 I have read that first order optimality should be close to zero. This is not achieved in my code. What does it mean? Is there a way to improve the results?

Thank you in advance.

[Matt J]

We'll probably need to see the objective function code.

Answer 1

[Alan Weiss]

This section of the documentation might be relevant.

Alan Weiss

MATLAB mathematical toolbox documentation

Answer 2

[Matt J]

Check the Hessian where the algorithm stops

 [x,fval,exitflag,output,lambda,grad,hessian]= fmincon(...)

If the Hessian is super-large (whether for good reasons or bad), that could explain why the algorithm takes super-small steps, even when the first-order derivatives are not small.

See also this similar post

http://www.mathworks.com/matlabcentral/answers/90090#comment_174180