Robust Markowitz Model

[Lissi]

I' m trying to implement a robust version of the markowitz model, but I have problems and various errors. I think my code is too simple. I tried to rewrite various times, but honestly I don't know what to change anymore.
I hope somebody could take a look at it and give me a hint. Perhaps I'm understanding the way yalmip works wrong,

% Test data
mu_t = [0.05; 0.11; 0.16; 0.25];
Sigma_t = [ 0.025 0.00055 0.0056 0.00125;
            0.00055 0.0121 -0.00352 0.011;
            0.0056 -0.00352 0.0256 0.012;
            0.00125 0.011 0.012 0.0625];

% Calculation of mu for the box contraint
mu_l = mu_t - 0.05*mu_t;
mu_u = mu_t + 0.05*mu_t;

% Calculation of Sigma for the box constraint
Sigma_l = Sigma_t - 0.05*Sigma_t;
Sigma_u = Sigma_t + 0.05*Sigma_t;

n = length(mu_t);
w = sdpvar(n,1);
mu = sdpvar(n,1);

sdpvar t1 t2 t3 t4
Sigma =     [t1, Sigma_t(1,2), Sigma_t(1,3), Sigma_t(1,4);
            Sigma_t(2,1), t2, Sigma_t(2,3), Sigma_t(2,4);
            Sigma_t(3,1), Sigma_t(3,2), t3, Sigma_t(3,4);
            Sigma_t(4,1), Sigma_t(4,2), Sigma_t(4,3), t4];

lambda = 0.5;

% constraints on the portfolio
W = [sum(w) == 1, w >= 0];

% Uncertainty set over the return vector - Box Constraint
M = [mu_l <= mu <= mu_u, uncertain(mu)];

% Uncertainty set over the covariance matrix - box constraint
S = [Sigma_l(1,1)<= t1 <= Sigma_u(1,1),
    Sigma_l(2,2)<= t2 <= Sigma_u(2,2),
    Sigma_l(3,3)<= t3 <= Sigma_u(3,3),
    Sigma_l(4,4)<= t4 <= Sigma_u(4,4),
    uncertain(t1), uncertain(t2), uncertain(t3), uncertain(t4)];



% objective function
objective = lambda*w'*Sigma*w - mu'*w;
solvesdp(W + S + M, objective)

solution = double(w)


Thanks!
Lissi

[Johan Löfberg]

Looks like a bug. Easily circumvented by

objective = lambda*w'*Sigma*w-mu'*w;
sdpvar t
solvesdp([W + S + M,lambda*w'*Sigma*w-mu'*w<=t] , t)

[Lissi]

Thank you! It's working!