Adaptive Inertial Method
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918028141133824 |
|---|---|
| author | Long, Han He, Bingsheng Ye, Yinyu Zhang, Jiheng |
| author_facet | Long, Han He, Bingsheng Ye, Yinyu Zhang, Jiheng |
| contents | In this paper, we introduce the Adaptive Inertial Method (AIM), a novel framework for accelerated first-order methods through a customizable inertial term. We provide a rigorous convergence analysis establishing a global convergence rate of O(1/k) under mild conditions, requiring only convexity and local Lipschitz differentiability of the objective function. Our method enables adaptive parameter selection for the inertial term without manual tuning. Furthermore, we derive the particular form of the inertial term that transforms AIM into a new Quasi-Newton method. Notably, under specific circumstances, AIM coincides with the regularized Newton method, achieving an accelerated rate of O(1/k^2) without Hessian inversions. Through extensive numerical experiments, we demonstrate that AIM exhibits superior performance across diverse optimization problems, highlighting its practical effectiveness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adaptive Inertial Method Long, Han He, Bingsheng Ye, Yinyu Zhang, Jiheng Optimization and Control 90C25, 90C30, 90C53, 65K10 In this paper, we introduce the Adaptive Inertial Method (AIM), a novel framework for accelerated first-order methods through a customizable inertial term. We provide a rigorous convergence analysis establishing a global convergence rate of O(1/k) under mild conditions, requiring only convexity and local Lipschitz differentiability of the objective function. Our method enables adaptive parameter selection for the inertial term without manual tuning. Furthermore, we derive the particular form of the inertial term that transforms AIM into a new Quasi-Newton method. Notably, under specific circumstances, AIM coincides with the regularized Newton method, achieving an accelerated rate of O(1/k^2) without Hessian inversions. Through extensive numerical experiments, we demonstrate that AIM exhibits superior performance across diverse optimization problems, highlighting its practical effectiveness. |
| title | Adaptive Inertial Method |
| topic | Optimization and Control 90C25, 90C30, 90C53, 65K10 |
| url | https://arxiv.org/abs/2505.15114 |