Accelerated Convergence of a Second-Order Dynamical System and its Application to Splitting Algorithms for Comonotone Inclusions
Abstract
This paper introduces a novel second-order dynamical system driven by a forward-backward splitting operator for solving the structured inclusion 0∈(A+B)(x) in a real Hilbert space, where A is a maximal ρ-comonotone operator and B is a ν-cocoercive operator. The well-posedness of the system is established, and Lyapunov analysis yields accelerated convergence rates of order o(1/t) for the velocity and o(1/t2) for the forward-backward residual, together with weak convergence of the trajectories to zer(A+B). Temporal discretization further leads to a class of double inertial Halpern forward-backward splitting algorithms that encompasses the classical forward-backward splitting method and its inertial variants as special cases. Numerical experiments on split feasibility, sparse signal recovery, and image deblurring illustrate the effectiveness of the proposed algorithm.
Related
- Accelerated Algorithms for Stochastic Monotone Inclusions with Fixed Queries
- Monte Carlo Power Iteration Algorithms: Convergence, Analysis and Application to Reactor Criticality Calculations
- Inexact Proximal Point and Tseng Algorithms with Nonsummable Errors to Solve Monotone Inclusions
- Weak and strong convergence of a general splitting approach for monotone multioperator inclusions
- Optimistic Gradient Algorithms with Randomized Coordinate and Variance Reduction Strategies for Composite Inclusions
BibTeX
@misc{tang2026accelerated,
title = {{Accelerated Convergence of a Second-Order Dynamical System and its Application to Splitting Algorithms for Comonotone Inclusions}},
author = {Yan Tang and Jun Dong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02479},
eprint = {2609.02479},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02479},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Accelerated Convergence of a Second-Order Dynamical System and its Application to Splitting Algorithms for Comonotone Inclusions
AU - Yan Tang
AU - Jun Dong
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02479
UR - https://arxiv.org/abs/2609.02479
AB - This paper introduces a novel second-order dynamical system driven by a forward-backward splitting operator for solving the structured inclusion 0∈(A+B)(x) in a real Hilbert space, where A is a maximal ρ-comonotone operator and B is a ν-cocoercive operator. The well-posedness of the system is established, and Lyapunov analysis yields accelerated convergence rates of order o(1/t) for the velocity and o(1/t^2) for the forward-backward residual, together with weak convergence of the trajectories to zer(A+B). Temporal discretization further leads to a class of double inertial Halpern forward-backward splitting algorithms that encompasses the classical forward-backward splitting method and its inertial variants as special cases. Numerical experiments on split feasibility, sparse signal recovery, and image deblurring illustrate the effectiveness of the proposed algorithm.
ER -