{"title":"An inertia projection method for nonlinear pseudo-monotone equations with convex constraints","authors":"Jinkui Liu, Ning Zhang, Bing Tang","doi":"10.1007/s11075-024-01934-5","DOIUrl":null,"url":null,"abstract":"<p>Based on DDP method proposed by Mohammad and Abubakar, in this paper we use the inertia index and relaxation factor to establish an inertia projection method for solving nonlinear pseudo-monotone equations with convex constraints. This method can generate a sufficient descent direction at each iteration, which is independent of any line search condition. Moreover, we prove the global convergence of the proposed method without assuming that the objective function satisfies the Lipschitz continuity. Numerical results demonstrate the effectiveness of the proposed method by comparing with some existing methods.</p>","PeriodicalId":54709,"journal":{"name":"Numerical Algorithms","volume":"21 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Algorithms","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11075-024-01934-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Based on DDP method proposed by Mohammad and Abubakar, in this paper we use the inertia index and relaxation factor to establish an inertia projection method for solving nonlinear pseudo-monotone equations with convex constraints. This method can generate a sufficient descent direction at each iteration, which is independent of any line search condition. Moreover, we prove the global convergence of the proposed method without assuming that the objective function satisfies the Lipschitz continuity. Numerical results demonstrate the effectiveness of the proposed method by comparing with some existing methods.
期刊介绍:
The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.