STABILIZED BARZILAI-BORWEIN METHOD  

作　　者：Oleg Burdakov Yuhong Dai Na Huang 

机构地区：[1]Department of Mathematics,Linkoping University,Linkoping,Sweden [2]LSEC,ICMSEC,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [3]Department of Applied Mathematics,College of Science,China Agricultural University,Beijing 100083,China

出　　处：《Journal of Computational Mathematics》2019年第6期916-936,共21页计算数学（英文）

基　　金：Part of this work was done during Oleg Burdakovs visit to the Chinese Academy of Sciences;which was supported by the Visiting Scientist award under the Chinese Academy of Sciences President's International Fellowship Initiative for 2017;The second author was supported by the Chinese Natural Science Foundation(No.11631013);the National 973 Program of China(No.2015CB856002).

摘　　要：The Barzilai-Borwein(BB)method is a popular and efficient tool for solving large-scale unconstrained optimization problems.Its search direction is the same as for the steepest descent(Cauchy)method,but its stepsize rule is different.Owing to this,it converges much faster than the Cauchy method.A feature of the BB method is that it may generate too long steps,which throw the iterates too far away from the solution.Moreover,it may not converge,even when the objective function is strongly convex.In this paper,a stabilization technique is introduced.It consists in bounding the distance between each pair of successive iterates,which often allows for decreasing the number of BB iterations.When the BB met hod does not converge,our simple modification of this method makes it convergent.For strongly convex functions with Lipsch计s gradients,we prove its global convergence,despite the fact that no line search is involved,and only gradient values are used.Since the number of stabilization steps is proved to be finite,the stabilized version inherits the fast local convergence of the BB met hod.The presented results of extensive numerical experiments show that our stabilization technique often allows the BB method to solve problems in a fewer计erations,or even to solve problems where the latter fails.

关 键 词：UNCONSTRAINED optimization SPECTRAL ALGORITHMS STABILIZATION CONVERGENCE analysis. 

分 类 号：O17[理学—数学]