KMS Of Academy of mathematics and systems sciences, CAS
| On the Asymptotic Convergence and Acceleration of Gradient Methods | |
| Huang, Yakui1; Dai, Yu-Hong2,3; Liu, Xin-Wei1; Zhang, Hongchao4 | |
| 2022 | |
| Source Publication | JOURNAL OF SCIENTIFIC COMPUTING
 |
| ISSN | 0885-7474 |
| Volume | 90Issue:1Pages:29 |
| Abstract | We consider the asymptotic behavior of a family of gradient methods, which include the steepest descent and minimal gradient methods as special instances. It is proved that each method in the family will asymptotically zigzag between two directions. Asymptotic convergence results of the objective value, gradient norm, and stepsize are presented as well. To accelerate the family of gradient methods, we further exploit spectral properties of stepsizes to break the zigzagging pattern. In particular, a new stepsize is derived by imposing finite termination on minimizing two-dimensional strictly convex quadratic function. It is shown that, for the general quadratic function, the proposed stepsize asymptotically converges to the reciprocal of the largest eigenvalue of the Hessian. Furthermore, based on this spectral property, we propose a periodic gradient method by incorporating the Barzilai-Borwein method. Numerical comparisons with some recent successful gradient methods show that our new method is very promising. |
| Keyword | Gradient methods Asymptotic convergence Spectral property Acceleration of gradient methods Barzilai-Borwein method Unconstrained optimization Quadratic optimization |
| DOI | 10.1007/s10915-021-01685-8 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11701137] ; National Natural Science Foundation of China[11631013] ; National Natural Science Foundation of China[12071108] ; National Natural Science Foundation of China[11671116] ; National Natural Science Foundation of China[11991021] ; National Natural Science Foundation of China[12021001] ; Strategic Priority Research Program of Chinese Academy of Sciences[XDA27000000] ; Beijing Academy of Artificial Intelligence (BAAI) ; Natural Science Foundation of Hebei Province[A2021202010] ; China Scholarship Council[201806705007] ; USA National Science Foundation[DMS-1819161] ; USA National Science Foundation[DMS-2110722] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000720653400002 |
| Publisher | SPRINGER/PLENUM PUBLISHERS |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/59572 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Zhang, Hongchao |
| Affiliation | 1.Hebei Univ Technol, Inst Math, Tianjin 300401, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA |
| Recommended Citation GB/T 7714 | Huang, Yakui,Dai, Yu-Hong,Liu, Xin-Wei,et al. On the Asymptotic Convergence and Acceleration of Gradient Methods[J]. JOURNAL OF SCIENTIFIC COMPUTING,2022,90(1):29. |
| APA | Huang, Yakui,Dai, Yu-Hong,Liu, Xin-Wei,&Zhang, Hongchao.(2022).On the Asymptotic Convergence and Acceleration of Gradient Methods.JOURNAL OF SCIENTIFIC COMPUTING,90(1),29. |
| MLA | Huang, Yakui,et al."On the Asymptotic Convergence and Acceleration of Gradient Methods".JOURNAL OF SCIENTIFIC COMPUTING 90.1(2022):29. |
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