Pareto Front Approximation through a Multi-objective Augmented Lagrangian Method

In this manuscript, we consider smooth multi-objective optimization problems with convex constraints. We propose an extension of a multi-objective augmented Lagrangian Method from recent literature. The new algorithm is specifically designed to handle sets of points and produce good approximations of the whole Pareto front, as opposed to the original one which converges to a single solution. We prove properties of global convergence to Pareto stationarity for the sequences of points generated by our procedure. We then compare the performance of the proposed method with those of the main state-of-the-art algorithms available for the considered class of problems. The results of our experiments show the effectiveness and general superiority w.r.t. competitors of our proposed approach.