On the Proximal Gradient Algorithm with Alternated Inertia

Franck Iutzeler (1) , Jérôme Malick (1)

1 DAO - Données, Apprentissage et Optimisation

In this paper, we investigate the attractive properties of the proximal gradient algorithm with inertia. Notably, we show that using alternated inertia yields monotonically decreasing functional values, which contrasts with usual accelerated proximal gradient methods. We also provide convergence rates for the algorithm with alternated inertia based on local geometric properties of the objective function. The results are put into perspective by discussions on several extensions and illustrations on common regularized problems.

Domaines: Optimisation et contrôle [math.OC]; Machine Learning [stat.ML]

Franck Iutzeler, Jérôme Malick. On the Proximal Gradient Algorithm with Alternated Inertia. Journal of Optimization Theory and Applications, 2018, 176 (3), pp.688-710. ⟨10.1007/s10957-018-1226-4⟩. ⟨hal-01685859⟩