I am currently working on problem that I think could be expressed as an integer lattice problem.

Given $u \in \mathbb{R}^n$ and a *bounded* integer lattice $L = \mathbb{Z}^n \cap [-M,M]^n$ I would like to find an integer vector $v \in L$ that minimizes the *angle* between $u$ and $v$. That is, I would like $$v \in \text{argmax}_{w \in L} \frac{u.w}{\|u\|\|w\|}$$

Here, the objective is maximizing the cosine of the angle between $u$ and $w$ (i.e. minimizing the angle between $u$ and $w$). The vectors $u$ and $w$ are said to be "similar" if this quantity is close to 1.

I am wondering:

Is this problem related to a well-known integer lattice problem (e.g. a closest vector problem)?

Could this problem be solved using existing lattice algorithms (e.g. the LLL algorithm?)