When maximizing mean-variance utility in a portfolio optimization framework
$max \{R - \lambda \sigma ^2\}$
where R is portfolio return, $\lambda$ is a risk aversion parameter, and $\sigma^2$ is portfolio volatility, how can I be sure that the result lies on the efficient frontier? I can show that $\lambda$ is effectively equals $\frac{R}{\sigma^2}$ but I don't quite see how this problem develops the efficient frontier