Partition array into k subsets
I'm assuming by $sum(i)$ you mean that given an ordering of the $k$ partitioned subsets, sum over all elements of the $i$th subset.

The $k=2$ case is the optimization variant of the set partitioning problem (https://en.wikipedia.org/wiki/Partition_problem) which is known to be as hard as subset sum. EDIT: The general case is as difficult by reduction from $k=2$.