Fmincon question:1.contraint violation but with no warning/error; 2. difference between the final output of Fmincon (the X in X=fmincon()) and the intermediate x

Hi All,

I found 2 pretty wired "features" of fmincon function when I was using fmincon to solve constrained optimization problems. First, it is very wired to have the difference between the final output of Fmincon (the X in X=fmincon()) and the intermediate x.

Second, I could see the nonlinear constraint is active meaning constraint is met but for the final result X outputted by X=fmicon(...) it does violate my nonlinear constraint. However, there is no error/warning at all.

I suppose that for the very last intermediate x and final output X should be the same theoretically. However, what I saw was not the case. They are very different.

I used active-set method in Fmincon. The document does mention that the active set method may violate the constraint in intermediate step. Sometimes I even saw the following case:

This is my last iterated u which is a function of my intermediate x (my upper limit for each element in vector u is 2 and you can see the third one from the bottom is way beyond 2):

u =

    2.0000
    2.0000
    2.0000
    2.0000
    2.0000
    2.0000
    2.0000
  188.7080
   -0.0000
    0.7391

This is the u I calculated by fmicon output X = fmincon and you can see how different they are compared to above intermediate u:

    2.0000
   22.9268
    2.0000
   15.7579
    2.0000
   16.2252
    2.0000
    2.0000
    2.0000
  996.8367

And here is what Matlab showed:

    Local minimum possible. Constraints satisfied.

fmincon stopped because the size of the current search direction is less than
twice the default value of the step size tolerance and constraints are 
satisfied to within the default value of the constraint tolerance.

Here is how I can tell my 11th to 20th constraints (the ones corresponds to my u) are active

    Active inequalities (to within options.TolCon = 1e-06):
  lower      upper     ineqlin   ineqnonlin
                                    11
                                    12
                                    13
                                    14
                                    15
                                    16
                                    17
                                    18
                                    19
                                    20

Here is what I mean by saying Final output and intermediate x:

Final output: the X in X=fmincon(),that is the final result generated outputted by fmincon function.

Intermediate x:the x used in cost function, nonlinear constraints function in fmincon. For example,

   X = fmincon(@cost_function,X0, [],[],[],[],[],[], @nonlinear_constraint); 
        % X is the final output

For the nonlinear constraint, I have

      function [c,ceq]=nonlinear_constraint(x)
        ...
        x % this is the intermediate x and this is how I can see the intermediate variable
      end

Cut long story short: 1.why does the results outputted by fmincon violate the constraints? 2.why are intermediate x and Fmincon output different? I was totally confused on this since these are not how things should work.

Thanks a lot! :)

Ji

Answer 1

[Alan Weiss]

It depends on how you are giving the upper bound. Is

 ub = 2*ones(size(x0))

or is

 ub = 2 ?

You need to give an upper bound for ever component of the solution. Clearly, from the exit message fmincon believes that the constraints are satisfied, so it does not know that you want all the elements to be bounded above by 2.

There is something else that might be going on. It seems that there might be a difference between your variable u that is larger than 2 and the control variable x (the one that fmincon is optimizing).

In any case, I suggest that you put a break point in fmincon and step through the program so that you can see if fmincon thinks that ub is a vector of all 2.

Alan Weiss

MATLAB mathematical toolbox documentation

[JI LIU]

Hi Alan,

Thanks for answering my question! And I am sorry for the confusion.

For my problem, I do not have any bounds on the control variable. The u in my question is a nonlinear function of x and I constrained u using nonlinear constraint.

X = fmincon(@costfunction,X0, [],[],[],[],[],[], @nonlinear_constraint);

I did try to add a break point in fmincon but I did not see any wired thing. Sometimes in the fmincon function very thing works just fine, but due to the output X given by fmicon is different from the x I saw inside fmincon I can see the output X violate the constraint.

Do you have any other thoughts on the difference between the control variable x (intermediate variable x) in fmincon and the output X outputted by fmincon? Thank you so much!

[Alan Weiss]

I am sorry, but I have a very hard time understanding you. So please be patient if my comment is not on point, because I get quite confused by your terminology.

In Optimization Toolbox, the control variables are typically called x. This is a vector or array that fmincon tries to change to minimize the objective function fun(x). Any intermediate values, which you seem to variously call u or X, are functions that your own program calculates.

Nonlinear constraints in fmincon have to be passed a particular way. I don't know how your nonlinear constraint function works or doesn't work. It seems to be allowing at least one component of your "u" (whatever that is) to take a value larger than you want. But fmincon doesn't see a constraint violation. Therefore I conclude that your nonlinear constraint does not restrict "u" the way you want it to. Check that function again.

Sorry, that is the best advice I can give you with the information you have provided.

Alan Weiss

MATLAB mathematical toolbox documentation