Development of a Lagrangean Dual Method for Solving Sequentially Connected 2D Assignment Problems: Modified deflected subgradient optimization and ergodic sequences

Abstract

This thesis addresses multi-object tracking (MOT) problems and studies efficient methods for evaluating the Trajectory Generalized Optimal Sub-Pattern Assignment (TGOSPA) metric. The primary objective is to develop a Lagrangian dual optimization method, that incorporates modified deflected sub-gradients and an enhanced ergodic sequence of subproblem solutions, and lastly constructing a feasible heuristic solution to the MOT problem. The proposed algorithm is evaluated on sequentially connected assignment problems of varying dimensions and tested against existing solution algorithms. While the algorithm demonstrates some potential, it exhibits sensitivity to parameter choices and suffers from slow convergence. Further refinement and development is therefore encouraged.