How can I find that the following type of problem is a convex of non-convex?
$\max_{x,y} \sum_{i \in N} r_{i,O} + \sum_{i \in K\setminus N} r_{i,L} $
The equation is taken from a paper I am reading. $r_{i,O}$ and $r_{i,L}$ are two different rates that are a variation of commonly known rate equation $R = B\log_2(1+SNR)$, where $B$ is the Bandwidth and $SNR$ is the Signal-to-Noise Ratio.
I am no expert in convex optimization (learning still), but this problem clearly looks non-convex based on the fact that the two subsets for $r_{i,O}$ and $r_{i,L}$ are clearly non intersecting.
For example, if $A = i \in N, B = i \in K \setminus N$ , then $A\cap B = \emptyset$.
Based on this, the problem is non-convex because for convexity, all points of a given problem should exist is one superset.