{"title":"New inertial forward–backward algorithm for convex minimization with applications","authors":"K. Kankam, W. Cholamjiak, P. Cholamjiak","doi":"10.1515/dema-2022-0188","DOIUrl":null,"url":null,"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.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":" ","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Demonstratio Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/dema-2022-0188","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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