Consider the following convex problem.
$\min{\mathbf{x}_1,\cdots,\mathbf{x}_N\in\mathbb{R}^K}\sum_{n=1}^Na_n f(\mathbf{x}_n)\\ s.t.\quad \sum_{n=1}^N\mathbf{x}_n=\mathbf{c},\\ 0\le \mathbf{x}_n \le 1$
where $f(\mathbf{x}_n)$ is convex w.r.t. $\mathbf{x}_n$, $a_n\ge 0, \mathbf{c}\in \mathbb{R}^K$.
Does anyone have some clues to solve this problem? (Suppose that this problem can not be solved by the CVX tool.)
By the way, can this problem be solved by multi -block ADMM or BCD?