Non-ergodic Convergence Analysis of Heavy-Ball Algorithms
arXiv:1811.01777
Abstract
In this paper, we revisit the convergence of the Heavy-ball method, and present improved convergence complexity results in the convex setting. We provide the first non-ergodic O(1/k) rate result of the Heavy-ball algorithm with constant step size for coercive objective functions. For objective functions satisfying a relaxed strongly convex condition, the linear convergence is established under weaker assumptions on the step size and inertial parameter than made in the existing literature. We extend our results to multi-block version of the algorithm with both the cyclic and stochastic update rules. In addition, our results can also be extended to decentralized optimization, where the ergodic analysis is not applicable.
References in corpus (6)
- Inertial Proximal Alternating Linearized Minimization (iPALM) for Nonconvex and Nonsmooth Problems
- Augmented L1 and Nuclear-Norm Models with a Globally Linearly Convergent Algorithm
- Asynchronous Coordinate Descent under More Realistic Assumptions
- Linearly convergent stochastic heavy ball method for minimizing generalization error
- iPiano: Inertial Proximal Algorithm for Non-Convex Optimization
- Quasinonexpansive Iterations on the Affine Hull of Orbits: From Mann's Mean Value Algorithm to Inertial Methods