Non-Acceleration of the Heavy-Ball Method in 1D
Despite having an asymptotically optimal rate of convergence on convex quadratics, the acceleration of Polyak's heavy-ball method and a characterization of its dynamics within more general settings have remained long standing open problems. Recently, the work of Goujaud et al. [Math. Program. (2025)] made progress regarding acceleration in the context of smooth, strongly convex minimization: for a small enough inverse condition number, either the method does not accelerate on quadratics, or there exists a smooth strongly convex function such that heavy-ball cycles over the roots of unity. The constructed functions have two variables, thus leaving the question of acceleration over univaria...
| Authors | Konstantinos Fotopoulos, Michael Helcig, Karl Deck et al. |
|---|---|
| Primary category | math.OC |
| Published | 18 October 2026 |
| Last updated at source | 18 October 2026 |
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