Alternative form of mean-variance optimization that uses standard deviation

I'm curious about an exercise found in Optimization Methods in Finance . Exercise 8.2 (pg 143) explores a variant of the more commonly used form of MVO. When I refer to the more common variant I'm talking about: $\begin{aligned} \operatorname{max}_x \mu^Tx - \frac{\delta}{2}x^T\Sigma x & \\ Ax &= b \\ Cx &\ge d \end{aligned}$ The variant that directly uses standard deviation by taking the square root of $x^T\Sigma x$ is: $$ \begin{aligned} \operatorname{max}_x \mu^Tx - \eta \sqrt{x^T\Sigma x