Derivation and Global Convergence for Memoryless Non-quasi-Newton Method  

作　　者：JIAO Bao Cong YU Jing Jing CHEN Lan Ping 

机构地区：[1]School of Mathematical Sciences, Capital Normal University, Beijing 100037, China [2]Department of Electrical Engineering, Qingdao Harbor Vocational Technology College, Shandong 266404, China

出　　处：《Journal of Mathematical Research and Exposition》2009年第3期423-433,共11页数学研究与评论（英文版）

基　　金：Foundation item： the National Natural Science Foundation of China （No. 60472071）; the Science Foundation of Beijing Municipal Commission of Education （No. KM200710028001）.

摘　　要：In this paper, a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved. Furthermore, we propose a hybrid method that mixes both the memoryless non-quasi-Newton method and the memoryless Perry-Shanno quasi-Newton method. The global convergence of this hybrid memoryless method is proved under mild assumptions. The initial results show that these new methods are efficient for the given test problems. Especially the memoryless non-quasi-Newton method requires little storage and computation, so it is able to efficiently solve large scale optimization problems.In this paper,a new class of memoryless non-quasi-Newton method for solving unconstrained optimization problems is proposed,and the global convergence of this method with inexact line search is proved.Furthermore,we propose a hybrid method that mixes both the memoryless non-quasi-Newton method and the memoryless Perry-Shanno quasi-Newton method.The global convergence of this hybrid memoryless method is proved under mild assumptions.The initial results show that these new methods are effcient for the given test problems.Especially the memoryless non-quasi-Newton method requires little storage and computation,so it is able to effciently solve large scale optimization problems.

关 键 词：memoryless non-quasi-Newton method Wolfe line search global convergence. 

分 类 号：O221.2[理学—运筹学与控制论] O224[理学—数学]