On the Proximal Gradient Algorithm with Alternated Inertia
This work addresses optimization challenges in machine learning by providing a method with guaranteed monotonicity, which is incremental compared to existing accelerated proximal gradient methods.
The paper tackles the problem of ensuring monotonic decrease in functional values for proximal gradient algorithms with inertia by introducing alternated inertia, achieving convergence rates based on local geometric properties of the objective function.
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.