Maximize function with constraints using fmincon

Hi guys, I want to max a function with constraints. I think fmincon would work but I don't know how to write it that it works.

    function [s] = objectfun1(w) 
           %thats the function, where w is unkown wheight vector of  
           %10 assets and M3 is constant CoskewnessMatrix

     s = w'*M3*kron(w,w);s=-s;

    end

    x0=zeros(10,1);
    Aeq=[1 1 1 1 1 1 1 1 1 1];

    beq=1;

    lb=zeros(10,1);

    ub=ones(10,1);

    w=fmincon(@objectfun1, x0, [], [], Aeq, beq,lb,ub)

Errors : _ _Undefined function or variable 'M3'.

Error in objectfun1 (line 3)
s = w'*M3*kron(w,w);s=-s;

Error in fmincon (line 545)
      initVals.f = feval(funfcn{3},X,varargin{:});

Error in testSkew (line 7)
w = fmincon(@objectfun1,zeros(10,1),[],[],[1 1 1 1 1 1 1 1 1 1],1,zeros(10,1),ones(10,1));

Caused by:
    Failure in initial user-supplied objective function evaluation. FMINCON cannot continue._ _

It should give me Max s and the coresponding weight vector. I would be glad for any help or the correct code :)

[Matt J]

It would be a little bit computationally cheaper to write the objective function as

      function [s] = objectfun1(w) 

           n=length(w);

           tmp=w.'*M3;

           s = -(w.'*reshape(tmp,n,n)*w);

      end

Answer 1

[Torsten]

1. M3 is not defined in objectfun1 ;

2. w'*M3*kron(w,w) does not look like a scalar value to me ;

3. Better delete the blanks in the call to fmincon.

Best wishes

Torsten.

[Marcel]

M3 is a constant matrix and loaded in the workspace. It is a known argument. How can I define it in the function correctly ?

[Matt J]

Torsten:

By inserting the line

global M3

at the positions where you define M3 and where you access M3

?

Best wishes

Torsten.

[Matt J]

Marcel

Ok I have changed it so far and I receive "only" 2 errors.

function [s,weight] = objectfun1(w3,M3)

s = w3'*M3*kron(w3,w3);s=-s;

weight = w3;

end

fun=objectfun1;

x0=zeros(10,1);

Aeq=[1 1 1 1 1 1 1 1 1 1];

beq=1;

lb=zeros(10,1);

ub=ones(10,1);

[w3, Sopt] = fmincon(fun,x0,Aeq,beq,lb,ub);

        Error using objectfun1 (line 4)
        Not enough input arguments.   (I need only w3 and M3 to compute s)

        Error in test4 (line 2)
        fun=objectfun1; (no idea ?)

I think the final solution cant be that far away.

Regards

[Matt J]

Torsten

function [s] = objectfun1(w,M)

    s=-w'*M*kron(w,w);           % As I told you: I doubt that w3'*M3*kron(w3,M3) is correct

   end

fun = @(w)objectfun1(w,M3);

x0=zeros(10,1);

Aeq=[1 1 1 1 1 1 1 1 1 1];

beq=1;

lb=zeros(10,1);

ub=ones(10,1);

[w3, Sopt] = fmincon(fun,x0,Aeq,beq,lb,ub);

Best wishes

Torsten.

[Matt J]

Guys, for the benefit of the rest of us, please reply to each other using the Comment boxes, instead of the Answer boxes. The Answer boxes are meant purely for starting threads for alternative answers.

[Marcel]

Hm ... when I run the script it says me :

    Error using fmincon (line 284)
    Aeq must have 10 column(s). (Doesn't make any sense)

    Error in test4 (line 14) 
    [w3, Sopt] = fmincon(fun,x0,Aeq,beq,lb,ub);

When I run the optimization tool it says "Not enough input arguments."

I think there is still something wrong with the function. Maybe fmincon is not appropriate but I dont know any better. Quadratic would be for a Covariance Matrix but in this case we have

s = -w'*M3*kron(w,w) not s=-w'*M3*w

I want to calculate the optimum Skewness Sopt and therefore need the weights (10x1). M3 is the CoSkewness Matrix (10x100).

[Matt J]

You're missing some input arguments,

     [w3, Sopt] = fmincon(fun,x0,[],[],Aeq,beq,lb,ub);

[Marcel]

Yes that is important and at the end this was the final mistake I made. I want to thank you both.