发表机构
School of Mathematics and Statistics, Chongqing Technology and Business University（重庆工商大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种新型二阶动力系统，经分析其具有加速收敛性，时间离散化后得到双惯性Halpern前向-后向分裂算法，数值实验验证了该算法在分裂可行性等问题上的有效性。
AI 中文摘要
本文提出一种由前向-后向分裂算子驱动的新型二阶动力系统，用于求解实希尔伯特空间中的结构化包含问题0∈(A+B)(x)，其中A是极大ρ-共单调算子，B是ν-余强制算子。本文建立了该系统的适定性，通过李雅普诺夫分析得到速度的收敛阶为o(1/t)、前向-后向残差的收敛阶为o(1/t²)，且轨迹弱收敛至zer(A+B)。时间离散化进一步得到一类双惯性Halpern前向-后向分裂算法，该算法包含经典前向-后向分裂方法及其惯性变体作为特例。针对分裂可行性、稀疏信号恢复和图像去模糊的数值实验验证了所提算法的有效性。
英文摘要
This paper introduces a novel second-order dynamical system driven by a forward-backward splitting operator for solving the structured inclusion $0\in(A+B)(x)$ 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 $o(\frac{1}{t})$ for the velocity and $o(\frac{1}{t^2})$ for the forward-backward residual, together with weak convergence of the trajectories to $\operatorname{zer}(A+B)$. 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.
