GLOBAL CONVERGENCE OF A CAUTIOUS PROJECTION BFGS ALGORITHM FOR NONCONVEX PROBLEMS WITHOUT GRADIENT LIPSCHITZ CONTINUITY  

作　　者：Gonglin YUAN Xiong ZHAO Jiajia YU 袁功林;赵雄;余家佳(School of Mathematics and Information Science,Center for Applied Mathematics of Guangxi(Guangxi University),Guangxi University,Nanning,530004,China)

机构地区：[1]School of Mathematics and Information Science,Center for Applied Mathematics of Guangxi(Guangxi University),Guangxi University,Nanning,530004,China

出　　处：《Acta Mathematica Scientia》2024年第5期1735-1746,共12页数学物理学报（B辑英文版）

基　　金：supported by the Guangxi Science and Technology base and Talent Project(AD22080047);the National Natural Science Foundation of Guangxi Province(2023GXNFSBA 026063);the Innovation Funds of Chinese University(2021BCF03001);the special foundation for Guangxi Ba Gui Scholars.

摘　　要：A cautious projection BFGS method is proposed for solving nonconvex unconstrained optimization problems.The global convergence of this method as well as a stronger general convergence result can be proven without a gradient Lipschitz continuity assumption,which is more in line with the actual problems than the existing modified BFGS methods and the traditional BFGS method.Under some additional conditions,the method presented has a superlinear convergence rate,which can be regarded as an extension and supplement of BFGS-type methods with the projection technique.Finally,the effectiveness and application prospects of the proposed method are verified by numerical experiments.

关 键 词：cautious BFGS nonconvex problems Lipschitz continuity projection technique global convergence 

分 类 号：O224[理学—运筹学与控制论]