MV Optimization can easily be expressed as a regression (OLS) problem. Firstly unconstrained: If you regress a (NX1 where N is the sample size) vector of ones on the asset returns, the relative regression coefficients are the same as the MVO weights, in fact they are the solution to the maximization of qudratic utility i.e. E[r]-risk_aversion*E[r^2]. So by changing the constant dependent variable we can arrive at weights that are exactly the same as MVO ones. If you solve MVO weights for a given risk aversion, them compute the portfolio mean and the portfolio variance, then the dependent variable in the regression will be [(mean^2+var)/mean]*ONE, where again ONE is an NX1 vector. Introducing constraints is convenient with any quadratic programming engine you have access to.

MV Optimization can easily be expressed as a regression (OLS) problem. 

Firstly unconstrained: If you regress a $N\times1$ (where $N$ is the sample size) vector of ones on the asset returns, the relative regression coefficients are the same as the MVO weights; in fact, they are the solution to the maximization of quadratic utility i.e. $E[r]-\text{risk_aversion}\times E[r^2]$. 

So by changing the constant dependent variable, we can arrive at weights that are exactly the same as MVO ones. If you solve MVO weights for a given risk aversion, then compute the portfolio mean and the portfolio variance, then the dependent variable in the regression will be $$\left[(\text{mean}^2+\text{var})/\text{mean}\right]\times\text{ONE}$$ where again $\text{ONE}$ is an $N\times1$ vector. 

Introducing constraints is convenient with any quadratic programming engine you have access to.