  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.
