I want to solve the following optimization problem:
$$ \max_{{\bf u}} \sum_{i=1}^N \left(a_i \textrm{ sign}({\bf u \ . x_i}) \right), $$
where ${\bf u}$ and ${\bf x_i}$ are $p\times1$ vectors, $a_i \in \{+1, -1, 0\}$ are known constants, and '$\cdot$' represents the vector inner product.
How can such problem be solved efficiently?
