Forward and reverse auction algorithms for Nonlinear Resource Allocation

We study the problem of optimally assigning N divisible resources to M competing tasks, where the performance cost of each task is a convex function of the resources allocated. This is called the Nonlinear Resource Allocation Problem (RAP). This class of problems arises in diverse fields such as search theory, statistics, finance, economics, logistics, sensor and wireless networks. In our recent work, we proposed a class of algorithms, RAP Auction, which were based on extensions of Auction algorithms for linear assignment problems. RAP Auction was shown to find a near optimal solution in finite time and converge under asynchronous computation. However, major limitations of RAP auction were the lack of stronger complexity results and mediocre empirical performance compared to alternative algorithms. In this paper, we develop a new class of algorithms for the solution RAP problems, based on the use of forward and reverse auction principles, along with scaling techniques. The new algorithms can be shown to have pseudo-polynomial complexity and are significantly faster in standard benchmarks than competing special purpose and general purpose state of the art methods.