{"title":"An approximate Newton-type proximal method using symmetric rank-one updating formula for minimizing the nonsmooth composite functions","authors":"Z. Aminifard, S. Babaie-Kafaki","doi":"10.1080/10556788.2022.2142587","DOIUrl":null,"url":null,"abstract":"Founded upon the scaled memoryless symmetric rank-one updating formula, we propose an approximation of the Newton-type proximal strategy for minimizing the nonsmooth composite functions. More exactly, to approximate the inverse Hessian of the smooth part of the objective function, a symmetric rank-one matrix is employed to straightly compute the search directions for a special category of well-known functions. Convergence of the given algorithm is argued with a nonmonotone backtracking line search adjusted for the corresponding nonsmooth model. Also, its practical advantages are computationally depicted in the two well-known real-world models.","PeriodicalId":124811,"journal":{"name":"Optimization Methods and Software","volume":"49 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Optimization Methods and Software","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/10556788.2022.2142587","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
Founded upon the scaled memoryless symmetric rank-one updating formula, we propose an approximation of the Newton-type proximal strategy for minimizing the nonsmooth composite functions. More exactly, to approximate the inverse Hessian of the smooth part of the objective function, a symmetric rank-one matrix is employed to straightly compute the search directions for a special category of well-known functions. Convergence of the given algorithm is argued with a nonmonotone backtracking line search adjusted for the corresponding nonsmooth model. Also, its practical advantages are computationally depicted in the two well-known real-world models.