Portfolio optimization too slow (Markowitz)

Hi guys!

I'working on some portfolio optimizations for my thesis and i have a little problem in the Mean-Variance approach. My work: I have a huge series of weekly returns (and weekly-average-prices), from 2010 to today, of 274 bonds (not all of them are issued in 2010); the idea is to divide this huge period (every 12 weeks) and watch what happened to the portfolio weights (and sigma and mu) accross periods. The division in period is a simple for, and it works for every function that i wrote. The only one approach that i think is not good is the Efficient-Frontier using portfolio object. I structured all the approches in function.

The problem is not that the function doesn't work, but it works too slow: I have a total of 40 iteration and at the 18th pass an eternity of time, then after the 23th I never see anything. The point of my MV optimization is that there are not short selling constraint, sum of weights is 1 and a good diversification, so some constraint in the upper bound.

function [MGV_weights MGV_mu MGV_sigma Weights_Max_Sharpe Max_Sharpe_sigma Max_Sharpe_mu Frontier_Risk Frontier_Ret] =...
    get_Efficient_Frontier(Sigma, Tot_Ret, nPort, index3, numAsset);

    DisplayFigure = 0; %1 = display, 0 = no display
    
    Total_Return = Tot_Ret(:, :)';
    [T N]   = size(Tot_Ret);
    
    mu=mean(Tot_Ret,2)';
    
    p = Portfolio('AssetMean', mu, 'AssetCovar', Sigma, 'LowerBound',...
        0, 'UpperBound',1*ub, 'Budget', 1);
    
    p.RiskFreeRate= 0;
    Weights_Max_Sharpe_temp = estimateMaxSharpeRatio(p);
    
    [Max_Sharpe_sigma, Max_Sharpe_mu] = estimatePortMoments(p, Weights_Max_Sharpe_temp);
    
    sigma = sqrt(diag(p.AssetCovar));
    [Weights_Frontier pbuy psell] = estimateFrontier(p,nPort);
    
    [Frontier_Risk Frontier_Ret] = plotFrontier(p, nPort);
    
    %% Uniform the length of outputs - this part is for the allocation in the for iter 
    MGV_weights_temp = Weights_Frontier(:,1);
    [MGV_sigma index] = min(Frontier_Risk); %sqrt(MGV_weights'*p.AssetCovar*MGV_weights)
    MGV_mu = min(MGV_weights_temp'*mu');
    
    Weights_Max_Sharpe = zeros(1,numAsset);
    Weights_Max_Sharpe([index3])= Weights_Max_Sharpe_temp;
    Weights_Max_Sharpe = Weights_Max_Sharpe';
    
    MGV_weights = zeros(1,numAsset);
    MGV_weights([index3])= MGV_weights_temp;
    MGV_weights = MGV_weights';
end

Sigma=variance covariance matrix; Tot_Ret=matrix of returns; nPort=number of portfolios that I want in the frontier; index3=is an index that catch only the position of the assets that are issued (if you run the code you can delete the row where there is index3), numAsset=is the number of TOTAL bond. ub is a number, for example 10% (not too low because in my iteration function in the beginning i have 17 assets).

My problem is on the functions "estimatePortMoments", "estimateMaxSharpeRatio", "estimateFrontier": it works, but too too slow... Anyone know how to speed up the optimization?

I tried also to use the quadprog function, but results are not as good as using portfolio object.

If I wasn't clear ask me! I know that there aree too many output and some part of the code is not optimal.

Thank you all!

Andrea