L1 norm regularization of Markowitz portfolio in matlab

Question

Markowitz portfolio with L1 norm regularization added L1 norm regularization based on the original model. The constraint equation is as follows:

The following code is the original Markowitz Mean-Variance model in matlab.

ExpReturn = [0.1 0.2 0.15];

ExpCovariance = [ 0.0100   -0.0061    0.0042
                 -0.0061    0.0400   -0.0252
                  0.0042   -0.0252    0.0225];
NumPorts = 4;

[PortRisk, PortReturn, PortWts] = frontcon(ExpReturn,ExpCovariance, NumPorts)

I have just started with Matlab and I don't know how to solve it in matlab.

Or is there any matlab code/toolbox to solve it? thank you!

Answer 1

You can decompose W in W+ and W- Where W = W+ + W- and W+>0 and W-<0. In that case, abs(W) = W+ - W-. That makes a problem 3x bigger but makes it easy to solve.