Derivation of Efficient Frontier (portfolio optimization) question

Question

In Robert Merton's derivation of the efficient frontier of a portfolio, he minimizes $\frac{1}{2}\sigma^2 $ over the investment weights in each asset, where $\sigma^2$ represents portfolio variance. I am confused why the function he minimizes is half the variance, instead of just the variance. It doesn't make a difference in calculations, but I cannot figure out why he (and all other derivations) do this.

Answer 1

It is simply a standard convention in quadratic programming to use the notation $\frac{1}{2}x^TQx + c^Tx + d$ for the objective. One reason for this is the fact that you get rid of a factor $2$ in the derivative, which now will be $Qx + c$. This cleans up the notation in the equations used for describing the solution algorithm.