KMS Of Academy of mathematics and systems sciences, CAS
| On the existence of affine invariant descent directions | |
| Dai, Yu-Hong1; Jarre, Florian2; Lieder, Felix3 | |
| 2020-03-24 | |
| Source Publication | OPTIMIZATION METHODS & SOFTWARE
 |
| ISSN | 1055-6788 |
| Pages | 17 |
| Abstract | 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. |
| Keyword | Affine invariance descent direction Newton direction |
| DOI | 10.1080/10556788.2020.1740221 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | Chinese NSF[11631013] ; Chinese NSF[11991021] |
| WOS Research Area | Computer Science ; Operations Research & Management Science ; Mathematics |
| WOS Subject | Computer Science, Software Engineering ; Operations Research & Management Science ; Mathematics, Applied |
| WOS ID | WOS:000524696100001 |
| Publisher | TAYLOR & FRANCIS LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51194 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Jarre, Florian |
| Affiliation | 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 |
| Recommended Citation 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. |
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