  We study a quadratic nonseparable resource allocation problem that arises in
the area of decentralized energy management (DEM), where unbalance in
electricity networks has to be minimized. In this problem, the given resource
is allocated over a set of activities that is divided into subsets, and a cost
is assigned to the overall allocated amount of resources to activities within
the same subset. We derive two efficient algorithms with $O(n\log n)$
worst-case time complexity to solve this problem. For the special case where
all subsets have the same size, one of these algorithms even runs in linear
time given the subset size. Both algorithms are inspired by well-studied
breakpoint search methods for separable convex resource allocation problems.
Numerical evaluations on both real and synthetic data confirm the theoretical
efficiency of both algorithms and demonstrate their suitability for integration
in DEM systems.
