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On the existence of affine invariant descent directions

文献类型：期刊论文

作者Dai, Yu-Hong3; Jarre, Florian2; Lieder, Felix1
刊名OPTIMIZATION METHODS & SOFTWARE
出版日期2020-03-24
页码17
关键词Affine invariance descent direction Newton direction
ISSN号1055-6788
DOI10.1080/10556788.2020.1740221
英文摘要This paper begins with a brief review of affine invariance and its significance for iterative algorithms. It then explores the existence of affine invariant descent directions for unconstrained minimization. While there may exist several affine invariant descent directions for smooth functions at a given point, it is shown that for quadratic functions, there exists exactly one invariant descent direction in the strictly convex case and generally none in the case where the Hessian is singular or indefinite. These results can be generalized to smooth nonlinear functions and have implications regarding the initialization of minimization algorithms. They stand in contrast to recent works on constrained convex and nonconvex optimization for which there may exist an affine invariant 'frame' that depends on the feasible set and that can be used to define an affine invariant descent direction.
资助项目Chinese NSF[11631013] ; Chinese NSF[11991021]
WOS研究方向Computer Science ; Operations Research & Management Science ; Mathematics
语种英语
WOS记录号WOS:000524696100001
出版者TAYLOR & FRANCIS LTD
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/51193]  
专题中国科学院数学与系统科学研究院
通讯作者Jarre, Florian
作者单位1.Heinrich Heine Univ Dusseldorf, Dusseldorf, Germany
2.Heinrich Heine Univ Dusseldorf, Dept Math, Dusseldorf, Germany
3.Chinese Acad Sci, Acad Math Syst Sci, Beijing, Peoples R China
推荐引用方式
GB/T 7714		 Dai, Yu-Hong,Jarre, Florian,Lieder, Felix. On the existence of affine invariant descent directions[J]. OPTIMIZATION METHODS & SOFTWARE,2020:17.
APA Dai, Yu-Hong,Jarre, Florian,&Lieder, Felix.(2020).On the existence of affine invariant descent directions.OPTIMIZATION METHODS & SOFTWARE,17.
MLA Dai, Yu-Hong,et al."On the existence of affine invariant descent directions".OPTIMIZATION METHODS & SOFTWARE (2020):17.

入库方式： OAI收割

来源：数学与系统科学研究院

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