当前位置: X-MOL 学术Optim. Methods Softw. › 论文详情
Analysis of the gradient method with an Armijo–Wolfe line search on a class of non-smooth convex functions
Optimization Methods & Software ( IF 1.431 ) Pub Date : 2019-10-09 , DOI: 10.1080/10556788.2019.1673388
Azam Asl; Michael L. Overton

It has long been known that the gradient (steepest descent) method may fail on non-smooth problems, but the examples that have appeared in the literature are either devised specifically to defeat a gradient or subgradient method with an exact line search or are unstable with respect to perturbation of the initial point. We give an analysis of the gradient method with steplengths satisfying the Armijo and Wolfe inexact line search conditions on the non-smooth convex function f(x)=a|x(1)|+∑i=2nx(i). We show that if a is sufficiently large, satisfying a condition that depends only on the Armijo parameter, then, when the method is initiated at any point x0∈Rn with x0(1)≠0, the iterates converge to a point x¯ with x¯(1)=0, although f is unbounded below. We also give conditions under which the iterates f(xk)→−∞, using a specific Armijo–Wolfe bracketing line search. Our experimental results demonstrate that our analysis is reasonably tight.
更新日期:2020-04-23

 

全部期刊列表>>
材料学研究精选
Springer Nature Live 产业与创新线上学术论坛
胸腔和胸部成像专题
自然科研论文编辑服务
ACS ES&T Engineering
ACS ES&T Water
屿渡论文,编辑服务
杨超勇
周一歌
华东师范大学
段炼
清华大学
中科大
唐勇
跟Nature、Science文章学绘图
隐藏1h前已浏览文章
中洪博元
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
ACS材料视界
x-mol收录
福州大学
南京大学
王杰
左智伟
电子显微学
何凤
洛杉矶分校
吴杰
赵延川
试剂库存
天合科研
down
wechat
bug