Mean Variance portfolio selection with l1-norm
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I have to find several efficient borders, applying to the markovitz model an l1-norm, so that the sum of the weights within the portfolio gives 1 and the sum of the weights in absolute value is less than or equal to a certain t-value. So I have to find the vector between t-min and t-max in such a way that the first one corresponds to a portfolio composed by only one asset with weight 1, and the second one to the portfolio uncostrained. Can I do this optimization through Quadprog?
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Matt J
on 29 Oct 2020
Sure. Minimizing a quadratic subject to linear constraints is exactly what quadprog is for.
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Matt J
on 29 Oct 2020
If you delete the first constraint, the problem as you've written it is solvable with quadprog in both x and u. However, with the first constraint included, and with both x and u unknown, it is no longer in the scope of quadprog.
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