A Unified Primal-Dual Recipe for Accelerating Three-Operator Splitting Methods
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911720219344896 |
|---|---|
| author | Sadiev, Abdurakhmon Condat, Laurent Richtárik, Peter |
| author_facet | Sadiev, Abdurakhmon Condat, Laurent Richtárik, Peter |
| contents | Composite optimization problems, formulated as the minimization of three functions, are ubiquitous in large-scale machine learning and signal processing. While state-of-the-art splitting methods such as Condat-Vũ (CV) [Condat, 2013, Vũ, 2013], Primal-Dual Davis-Yin (PDDY) [Salim et al., 2022b], and Primal-Dual Twice Reflected (PDTR) [Malitsky and Tam, 2026] are highly versatile, they inherently exhibit non-accelerated convergence rates. Existing accelerated primal-dual splitting results either focus on special structures like one of the functions being zero, or linearly constrained problems, or smooth regimes, or directly use Nesterov-type momentum. Our contribution is a unified Bregman primal-dual framework that yields four variants and a common Lyapunov analysis. By applying the Chambolle-Pock algorithm [Chambolle and Pock, 2011] to primal-dual reformulations, we systematically derive four novel accelerated algorithms: Accelerated Condat-Vũ (ACV-I and ACV-II) and Accelerated Primal-Dual Twice Reflected (APDTR-I and APDTR-II). Through a simplified Lyapunov-based analysis, we establish iteration complexities for both smooth and nonsmooth cases, successfully removing the restrictive assumptions restrictions required by prior works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_26985 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified Primal-Dual Recipe for Accelerating Three-Operator Splitting Methods Sadiev, Abdurakhmon Condat, Laurent Richtárik, Peter Optimization and Control Composite optimization problems, formulated as the minimization of three functions, are ubiquitous in large-scale machine learning and signal processing. While state-of-the-art splitting methods such as Condat-Vũ (CV) [Condat, 2013, Vũ, 2013], Primal-Dual Davis-Yin (PDDY) [Salim et al., 2022b], and Primal-Dual Twice Reflected (PDTR) [Malitsky and Tam, 2026] are highly versatile, they inherently exhibit non-accelerated convergence rates. Existing accelerated primal-dual splitting results either focus on special structures like one of the functions being zero, or linearly constrained problems, or smooth regimes, or directly use Nesterov-type momentum. Our contribution is a unified Bregman primal-dual framework that yields four variants and a common Lyapunov analysis. By applying the Chambolle-Pock algorithm [Chambolle and Pock, 2011] to primal-dual reformulations, we systematically derive four novel accelerated algorithms: Accelerated Condat-Vũ (ACV-I and ACV-II) and Accelerated Primal-Dual Twice Reflected (APDTR-I and APDTR-II). Through a simplified Lyapunov-based analysis, we establish iteration complexities for both smooth and nonsmooth cases, successfully removing the restrictive assumptions restrictions required by prior works. |
| title | A Unified Primal-Dual Recipe for Accelerating Three-Operator Splitting Methods |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.26985 |