Auction Algorithm for Nonlinear Resource Allocation Problems

We study the problem of optimally assigning N divisible resources to M competing missions/tasks. We call this the Nonlinear Resource Allocation Problem (RAP). This simple yet powerful framework has found applications in diverse fields such as search theory, statistics, finance, economics, logistics, sensor and wireless networks. RAP is an instance of convex program but it has a bipartite structure like the assignment/transportation problem. In this paper, we propose a new algorithm, RAP Auction, for this problem which finds a near optimal solution in finite time. Unlike most existing methods in literature, we do not presuppose a particular cost function or assume differentiability or strict convexity. RAP Auction works for any monotonic convex cost function. It has a very simple computation structure amenable to distributed implementation.