New inertial forward–backward algorithm for convex minimization with applications

IF 2 3区数学 Q1 MATHEMATICS

Demonstratio Mathematica Pub Date : 2023-01-01 DOI:10.1515/dema-2022-0188

K. Kankam, W. Cholamjiak, P. Cholamjiak

引用次数: 0

Abstract

Abstract In this work, we present a new proximal gradient algorithm based on Tseng’s extragradient method and an inertial technique to solve the convex minimization problem in real Hilbert spaces. Using the stepsize rules, the selection of the Lipschitz constant of the gradient of functions is avoided. We then prove the weak convergence theorem and present the numerical experiments for image recovery. The comparative results show that the proposed algorithm has better efficiency than other methods.

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一种新的凸极小化惯性前向-后向算法及其应用

摘要在这项工作中，我们提出了一种新的基于Tseng的外梯度方法和惯性技术的近梯度算法来解决实Hilbert空间中的凸最小化问题。利用步长规则，避免了函数梯度的Lipschitz常数的选取。然后，我们证明了弱收敛定理，并给出了图像恢复的数值实验。比较结果表明，该算法比其他方法具有更好的效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Demonstratio Mathematica MATHEMATICS-

CiteScore

2.40

自引率

5.00%

发文量

审稿时长

35 weeks

期刊介绍： Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.