MATLAB: Is fmincon ending in points it knows are sub-optimal

fminconoptimization

So I'm running fmincon on some complex function.

                                            First-order      Norm of
 Iter F-count            f(x)  Feasibility   optimality         step
    0       6    1.264764e+04    0.000e+00    6.529e+09
    1      13   -3.111363e+04    0.000e+00    1.043e+10    1.485e+01
    2      19   -3.413651e+04    0.000e+00    7.615e+09    8.769e+03
    3      25   -3.861130e+04    0.000e+00    1.613e+09    6.264e+02
    4      34   -3.840241e+04    0.000e+00    1.376e+09    9.530e-03
    5      41   -3.843143e+04    0.000e+00    5.582e+09    9.954e-01

I get this and it ends there at Iteration 5, returning the parameter values of that iteration and calling it an optimum. However, clearly, iteration 3 had found a superior feasable solution.

Any clue as to why this is happening? And how to stop that? The program that ultimately calls on fmincon is a complex code written by someone else, that I don't understand fully. Could he have put some option to stop fmincon from returning the values at iteration 3 instead of the ones at the last iteration?

Best Answer

It appears that the first-order optimality measure is nowhere near zero, so I am sure that fmincon does not claim that it reached a minimum. It probably stopped because the norm of the step was too small, meaning it could not proceed. For suggestions on what to do in this case, see Local Minimum Possible.

Alan Weiss

MATLAB mathematical toolbox documentation

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MATLAB: When I am running a fmincon function, I am getting this following result. After checking, I was able to find out that there are 10 cg iterations taking place at every iteration of fmincon. Is it possible for us to view the cg iteration values

There is no documented way that I am aware of in fmincon or optimoptions to view the CG iterations.

MATLAB: Trying to minimise a function subject to nonlinear constraints

Simple mistake(s) here. You have TWO equality constraints. But your constraint function is written to have ONE equality constraint, and ONE inequality constraint. And you also wrote the x*z=3 constraint wrong. You wrote it as y*z=3.

Instead, try this:

function [c,ceq] = confuneq(x)
    c = [];
    ceq = [x(2)^2+x(3)^2-1; x(1)*x(3)-3];
end

That should now be a correct way to write the constraints.

Of course, don't expect fmincon to provide both solutions in one call. You need to start the optimizer out in the correct basin of attraction to get the solution you might want to see.

x = fmincon(fun,[1 1 2],A,b,Aeq,beq,lb,ub,nonlcon,options)
 Iter  Func-count            Fval   Feasibility   Step Length       Norm of   First-order  
                                                                       step    optimality
    0           4    3.000000e+00     4.000e+00     1.000e+00     0.000e+00     2.000e+00  
    1           9    2.928889e+00     3.352e+00     7.000e-01     1.504e+00     9.644e-01  
    2          13    2.571265e+00     7.559e-01     1.000e+00     1.060e+00     3.470e-01  
    3          17    2.789068e+00     2.110e-01     1.000e+00     7.947e-01     3.581e-01  
    4          21    2.988095e+00     1.191e-02     1.000e+00     3.066e-01     4.893e-02  
    5          25    2.999988e+00     1.161e-05     1.000e+00     1.437e-02     9.121e-04  
    6          29    3.000000e+00     5.045e-09     1.000e+00     7.238e-05     1.451e-04  
    7          33    3.000000e+00     5.265e-09     1.000e+00     7.255e-05     1.646e-07  
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
<stopping criteria details>
x =
          2.99999999210178     -1.73125747607761e-08          1.00000000263274
          
>> x = fmincon(fun,[-1 1 0],A,b,Aeq,beq,lb,ub,nonlcon,options)
 Iter  Func-count            Fval   Feasibility   Step Length       Norm of   First-order  
                                                                       step    optimality
    0           4    1.000000e+00     3.000e+00     1.000e+00     0.000e+00     2.000e+00  
    1          12    1.720300e+00     2.280e+00     2.401e-01     7.203e-01     1.520e+00  
    2          19    1.688289e+00     1.455e+00     3.430e-01     9.684e-01     6.358e-01  
    3          23    2.587102e+00     4.133e-01     1.000e+00     1.342e+00     6.046e-01  
    4          27    2.929079e+00     7.341e-02     1.000e+00     6.240e-01     2.038e-01  
    5          31    3.000225e+00     6.050e-04     1.000e+00     9.457e-02     5.761e-02  
    6          35    3.000027e+00     5.576e-04     1.000e+00     2.362e-02     1.620e-02  
    7          39    3.000000e+00     2.761e-05     1.000e+00     5.308e-03     4.556e-04  
    8          43    3.000000e+00     2.435e-09     1.000e+00     6.453e-05     2.124e-05  
    9          47    3.000000e+00     0.000e+00     1.000e+00     4.398e-09     1.192e-06  
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.
<stopping criteria details>
x =
         -3.00000000000053      5.92273862321821e-07        -0.999999999999825

Best Answer

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MATLAB: When I am running a fmincon function, I am getting this following result. After checking, I was able to find out that there are 10 cg iterations taking place at every iteration of fmincon. Is it possible for us to view the cg iteration values

MATLAB: Trying to minimise a function subject to nonlinear constraints

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