新型类fista算法的收敛与应用

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-04-24 DOI:10.1016/j.cnsns.2025.108871

Yeyu Zhang , Hongwei Liu , Yan Tang

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引用次数: 0

摘要

本文提出了一种新的类似快速迭代收缩阈值算法（FISTA）的统一框架，用于解决实际Hilbert空间中的非光滑凸最小化问题，该框架包括正向向后分裂方法、惯性正向向后算法和FISTA算法。研究了目标函数的收敛速度和迭代算法，在目标函数一致凸的条件下，得到了该算法的强收敛性。其次，提出了一种类似fista算法的摄动版本。介绍了两种步长选择策略和改进算法局部振荡行为的措施，极大地提高了算法的实际应用性能。此外，建立了连续动力系统的模型，并得到了系统的渐近性质。最后，通过LASSO问题、图像去模糊和信号恢复验证了所提算法的有效性和优越性。

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Convergence and applications of novel FISTA-like algorithms

In this paper, a novel unified framework of fast iterative shrinkage-thresholding algorithm (FISTA)-like algorithms is proposed for nonsmooth convex minimization problems in real Hilbert spaces, which includes several variants (e.g., forward–backward splitting methods, inertial forward–backward algorithms, and FISTA). The convergence rates of the objective function and the iterative algorithm are studied, and the strong convergence is obtained provided that the objective function is uniformly convex. Secondly, a perturbed version of the FISTA-like algorithms is presented. Two strategies for the selection of the step size and improvement measures for the local oscillation behavior of the algorithm are introduced, which greatly improves the practical application performance. In addition, the model of the continuous dynamical system is established, and also the asymptotic property is obtained. Finally, the effectiveness and superiority of the proposed algorithms are verified by LASSO problems, image deblurring, and signal recovery.

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.