Let $A \in \mathbb{R}^{n \times m}$, $b \in \mathbb{R}^n$. Suppose $m \ll n$. How to solve $\min_{x \in \mathbb{R}^n} b^\top x + \frac{1}{2} x^\top AA^\top x$ efficiently?

Let $A \in \mathbb{R}^{n \times m}$ and $b \in \mathbb{R}^n$. Suppose $m \ll n$. How to solve this quadratic program efficiently?

$$\min_{x \in \mathbb{R}^n} \frac{1}{2} x^\top AA^\top x + b^\top x$$

Let $A \in \mathbb{R}^{n \times m}$, $b \in \mathbb{R}^n$. Suppose $m \ll n$. How to solve the linear system $AA^\top x = b$ efficiently?

Let $A \in \mathbb{R}^{n \times m}$, $b \in \mathbb{R}^n$. Suppose $m \ll n$. How to solve $\min_{x \in \mathbb{R}^n} b^\top x + \frac{1}{2} x^\top AA^\top x$ efficiently?