The randomized block coordinate descent method in the Hölder smooth setting

We analyze randomized block coordinate descent for objective functions satisfying Hölder smoothness and block Hölder smoothness conditions. The analysis covers nonconvex, convex, and strongly convex optimization, establishing convergence rates for the expected gradient norm or objective suboptimality as appropriate.

These results extend convergence guarantees beyond the standard Lipschitz smooth setting and recover the established rates in that setting, including linear convergence for strongly convex objectives.

Recommended citation: Farias Maia, L., & Gutman, D. H. (2025). The randomized block coordinate descent method in the Hölder smooth setting. Optimization Letters, 19, 1–20. https://doi.org/10.1007/s11590-024-02161-6