On the existence of affine invariant descent directions

doi:10.1080/10556788.2020.1740221

CSpace

	On the existence of affine invariant descent directions
	Dai, Yu-Hong 1; Jarre, Florian 2; Lieder, Felix 3
	2020-03-24
发表期刊	OPTIMIZATION METHODS & SOFTWARE
ISSN	1055-6788
页码	17
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.
关键词	Affine invariance descent direction Newton direction
DOI	10.1080/10556788.2020.1740221
收录类别	SCI
语种	英语
资助项目	Chinese NSF[11631013] ; Chinese NSF[11991021]
WOS研究方向	Computer Science ; Operations Research & Management Science ; Mathematics
WOS类目	Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000524696100001
出版者	TAYLOR & FRANCIS LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51194
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.Chinese Acad Sci, Acad Math Syst Sci, Beijing, Peoples R China 2.Heinrich Heine Univ Dusseldorf, Dept Math, Dusseldorf, Germany 3.Heinrich Heine Univ Dusseldorf, Dusseldorf, Germany
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.