  In this manuscript, we address continuous unconstrained optimization problems
and we discuss descent type methods for the reconstruction of the Pareto set.
Specifically, we analyze the class of Front Descent methods, which generalizes
the Front Steepest Descent algorithm allowing the employment of suitable,
effective search directions (e.g., Newton, Quasi-Newton, Barzilai-Borwein). We
provide a deep characterization of the behavior and the mechanisms of the
algorithmic framework, and we prove that, under reasonable assumptions,
standard convergence results and some complexity bounds hold for the
generalized approach. Moreover, we prove that popular search directions can
indeed be soundly used within the framework. Then, we provide a completely
novel type of convergence results, concerning the sequence of sets produced by
the procedure. In particular, iterate sets are shown to asymptotically approach
stationarity for all of their points; additionally, in finite precision
settings, the sets are shown to only be enriched through exploration steps in
later iterations, and suitable stopping conditions can be devised. Finally, the
results from a large experimental benchmark show that the proposed class of
approaches far outperforms state-of-the-art methodologies.
