A Dual- Ascent Algorithm for the Multi-dimensional Assignment Problem: Application to Multi-Target Tracking

Recently we proposed a new Mixed-Integer Linear Programming formulation for the Multi-Target Tracking (MTT) problem and used a standard optimization solver to demonstrate its viability [1]. Subsequently, we provided Graphics Processing Unit (GPU) accelerated algorithms for the underlying Multidimensional Assignment Problem (MAP) with decomposable costs or triplet costs using a Lagrangian Relaxation (LR) framework. Here, we present a Dual-Ascent algorithm that provides monotonically increasing lower bounds and converges in a fraction of iterations required for a subgradient scheme. This approach can handle a large number of targets for many time steps with massive parallelism and computational efficiency. The dual-ascent framework decomposes the MAP into a set of Linear Assignment Problems (LAPs) for adjacent time-steps, which can be solved in parallel using the GPU-accelerated method of [2], [3]. The overall dual-ascent algorithm is able to efficiently solve problems with 100 targets and 100 time-frames with high accuracy. We demonstrate the applicability of our new algorithm to MTT by including realistic issues of missed detections and false alarms. Computational results demonstrate the robustness of the algorithm with good MMEP and ITCP scores and solution times for the larger problems in less than 6 seconds.