Constraints not meeting the parameters?

Hello:

This is what my code looks like for the the linear equality constraints. However, run I run the code it does not meet the constraints.

in swtOther_Aeq1, the first constraint is to make stocks 1,3,7 comprise 22% of the portfolio.

the second constraint is to make the portfolio return equal to a certain return in the grid (ERGRid).

the third constraint is to have the total weights sum up to one for the portfolio.

However, none of these requirements are being met.

I am confused as to why.

Help would be appreciated. thanks.

[Matt J]

What does the exitflag output argument say?

And how much greater is the constraint violation than options.TolCon?

[Sameer]

Exitflag says 0.04044

output says -2

[Sameer]

Also this is what TolCon says:

TolCon =

         iterations: 29
          funcCount: 337
    constrviolation: 9.3468
           stepsize: 7.6372e-11
          algorithm: 'interior-point'
      firstorderopt: 0.059526
       cgiterations: 58
            message: 'No feasible solution found.

fmi...'

Answer 1

[Matt J]

Exitflag=-2 means that no feasible point was found, as output.message also tells you. It means fmincon thinks there is no point satisfying your constraints.

[Sameer]

It says output = -2 and exitflag is 0.04044. I read

http://www.mathworks.com/help/optim/ug/exit-flags-and-exit-messages.html

that a positive exitflag means a successful outcome.

[Matt J]

No, exitflag has to be an integer and output has to be a structure. You just called fmincon with the output arguments named in the wrong order. It doesn't matter. This output,

          iterations: 29
          funcCount: 337
    constrviolation: 9.3468
           stepsize: 7.6372e-11
          algorithm: 'interior-point'
      firstorderopt: 0.059526
       cgiterations: 58
            message: 'No feasible solution found.

gives a message clearly stating 'No feasible solution found'. It tells us everything we need to know.

[Sameer]

Interesting. My teacher gave this to us as a homework assignment. He says the program should run without constraint problems.

Do you know what he may have done? I heard there are options you may use to modify the tolerance of the constraints?

[Matt J]

I heard there are options you may use to modify the tolerance of the constraints?

This is the TolCon option. However, I would first consider whether you have entered the data for the constraints incorrectly.

You can also try LCON2VERT to find the vertices of the region defined by your A,b,Aeq,beq,ub,lb constraint data. If the set of vertices V is empty, you know that your constraints are infeasible. Note, however, that you would have to convert your ub,lb data to ineqaulity constraint form.

[Sameer]

%options(1) = 1; % 1 = turn on screen, 0 = off, -1 = surpress warning messages

%options (2) = le-5; % tollerance for weights, default = le-4

%options(3) = le-5; % tollerance for objective function, default = le-4

these are the three options my teacher suggested we use in the program. I tried using option 2 with

options = optimset('TolCon',1e-5);

 but it did not give me a feasible solution.

[Sameer]

sorry I'm new to MATLAB, but I want to understand how it works.

[Matt J]

As I said, I would not look to TolCon or any of the other option settings as prime suspects for why things are not working. I would look to your constraint data.

[Sameer]

If you look at the third constraint, when I write (i is the loop variable)

swtOther_Aeq1 = ERGrid(2:swtN+1,i)';

swtOther_beq1 = 1.00;

and do not use any other constraints in fmincon, the program runs and says it finds a solution, but when I sum up W (the weights in a portfolio) it does not sum up to 1.

Instead, it sums to -0.1001.

It should some to 1.00, given vector multiplication.

[Sameer]

However, when I entered

swtOther_beq = (-1.00*10)+0.01,

the portfolio weights in a bizzare fashion sums to 1.00.

I am confused on the rationale

[Sameer]

nevermind, I figured it out. teacher used different constraints!

However the bizarreness is still confusing.