MATLAB: Fmincon with Nested Optimization

constrained optmizationfminconsharpe ratio

I have to maximize the sharpe ratio, but my weights are given by an equation. I am not knowing how to connect that with fmincon
function [y] = w2(a) %function for weight
global avrcc avrco avroc avroo avrrvp avrtvl rcc rco roc roo tvl rvp i j n
y = a(1)*(rcc(i-1,j)-avrcc(i-1))./n...
    + a(2)*(roo(i,j)-avroo(i))./n...
    + a(3)*(roc(i-1,j)-avroc(i-1))./n ...
    + a(4)*(rco(i,j)-avrco(i))./n...
    + a(5)*(tvl(i-1,j)/avrtvl(i-1,j))*(rcc(i-1,j)-avrcc(i-1))./n...
    + a(6)*(tvl(i-1,j)/avrtvl(i-1, j))*(roo(i,j)-avroo(i))./n...
    + a(7)*(tvl(i-1,j)/avrtvl(i-1,j))*(roc(i,j)-avroc(i-1))./n...
    + a(8)*(tvl(i-1,j)/avrtvl(i-1,j))*(rco(i,j)-avrco(i))./n...
    + a(9)*(rvp(i-1,j)/avrrvp(i-1,j))*(rcc(i-1,j)-avrcc(i-1))./n...
    + a(10)*(rvp(i-1,j)/avrrvp(i-1,j))*(roo(i,j)-avroo(i))./n...
    + a(11)*(rvp(i-1,j)/avrrvp(i-1,j))*(roc(i-1,j)-avroc(i-1))./n...
    + a(12)*(rvp(i-1,j)/avrrvp(i-1,j))*(rco(i,j)-avrco(i))./n;
end
My function for sharpe ratio is as follows
function [y] = msharper(mu,Q,rf)
y = mu-rf/sqrt(w2(a)'*Q*w2(a));
end
I do not know how to apply fmincon such a way that I find the values of a vector.

Best Answer

My approach would be to modify the functions as follows, taking into account Walter's remarks and also getting rid of the global variables,
    function [y] = w2(a,   avrcc, avrco, avroc, avroo, avrrvp,...
                           avrtvl, rcc, rco, roc, roo, tvl, rvp, i, j, n)
    y = a(1)*(rcc(i-1,j)-avrcc(i-1))./n...
        + a(2)*(roo(i,j)-avroo(i))./n...
        + a(3)*(roc(i-1,j)-avroc(i-1))./n ...
        + a(4)*(rco(i,j)-avrco(i))./n...
        + a(5)*(tvl(i-1,j)/avrtvl(i-1,j))*(rcc(i-1,j)-avrcc(i-1))./n...
        + a(6)*(tvl(i-1,j)/avrtvl(i-1, j))*(roo(i,j)-avroo(i))./n...
        + a(7)*(tvl(i-1,j)/avrtvl(i-1,j))*(roc(i,j)-avroc(i-1))./n...
        + a(8)*(tvl(i-1,j)/avrtvl(i-1,j))*(rco(i,j)-avrco(i))./n...
        + a(9)*(rvp(i-1,j)/avrrvp(i-1,j))*(rcc(i-1,j)-avrcc(i-1))./n...
        + a(10)*(rvp(i-1,j)/avrrvp(i-1,j))*(roo(i,j)-avroo(i))./n...
        + a(11)*(rvp(i-1,j)/avrrvp(i-1,j))*(roc(i-1,j)-avroc(i-1))./n...
        + a(12)*(rvp(i-1,j)/avrrvp(i-1,j))*(rco(i,j)-avrco(i))./n;
    end
    function [y] = msharper(a, mu,Q,rf,weightfun)
       y = mu-rf/sqrt(weightfun(a)'*Q*weightfun(a));
    end
and then in the main workspace,
   weightfun=@(a) w2(a,   avrcc, avrco, avroc, avroo, avrrvp,...
                           avrtvl, rcc, rco, roc, roo, tvl, rvp, i, j, n);
   a_opt = fmincon @(a)  msharper(a, mu,Q,rf,weightfun),    __________  );
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