How to implement a nonlinear constraint?

hello i would appreciate some help to implement a nonlinear inequality in my fmincon program. I am trying to maximize Sharpe ratio under two constraints. First that the sum of the weights equal one and the second one is that (((w-w0).^2).^1/2) -0.005 >= 0 (tracking error constraint where w0 is set to be the benchmark weights vector). I am getting errors when trying to programme the tracking error constraint. Thank you!

    for i=1:T-M    
    objective = @(w) -(zbarA3(:,i)'*w - rf)/(sqrt(w'*covmatA3{1,i}*w));
    w0 = Wi_AQ2;
    Aeq = ones(1,n);
    beq = 1;
    W_Q3(:,i) = fmincon(objective,w0,[],[],Aeq,beq,[],[],nonling);
    end 

    %where nonling is 
    function [c,ceq]=nonling(w)
    c= sqrt((w(1) - Wi_AQ2)^2) -0.005;
    ceq=w*0;
    end

[Matt J]

Please indent your code (but not your text) to make it more readable.

[Mohamad Moussa]

Fixed, sorry for that first time asking.

[Matt J]

Is this

   (((w-w0).^2).^1/2)

really in fact supposed to be

norm(w-w0)

?

[Mohamad Moussa]

It is supposed to take the absolute value of the difference.

[Matt J]

w and w0 are length-n vectors. Do you therefore have n contraints?

abs(w(i)-w0(i))>=0.005, i=1...,n

[Mohamad Moussa]

True i did not notice that oppositely to Aeq and Beq, c and ceq right side in the inequality is a scaler not a vector. Maybe this should do the trick if not ill try making a loop like you stated previously. Thank you

 function [c,ceq]=nonling(w,w0)
      c= abs(w - w0)*ones(1,n) -0.005;
      ceq=[];
    end

Answer 1

[Matt J]

    for i=1:T-M    
    objective = @(w) -(zbarA3(:,i)'*w - rf)/(sqrt(w'*covmatA3{1,i}*w));
    w0 = Wi_AQ2;
    Aeq = ones(1,n);
    beq = 1;
    W_Q3(:,i) = fmincon(objective,w0,[],[],Aeq,beq,[],[], @(w) nonling(w,w0) );
    end 

    function [c,ceq]=nonling(w,w0)

      c= .005^2-norm(w - w0)^2 ;
      ceq=[];

    end

[Mohamad Moussa]

Thank you for the help and fast response time!