SONC optimization and exact nonnegativity certificates via second-order cone programming
文献类型：期刊论文
| 作者 | Magron, Victor1,2; Wang, Jie3 |
| 刊名 | JOURNAL OF SYMBOLIC COMPUTATION
 |
| 出版日期 | 2023-03-01 |
| 卷号 | 115页码:346-370 |
| 关键词 | Sum of nonnegative circuit polynomials Second -order cone programming Polynomial optimization Sum of binomial squares Rounding -projection algorithm Exact nonnegativity certificate |
| ISSN号 | 0747-7171 |
| DOI | 10.1016/j.jsc.2022.08.002 |
| 英文摘要 | The second-order cone (SOC) is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in theory and in practice to investigate which convex cones admit a representation using SOCs, given that they have a strong expressive ability. In this paper, we prove constructively that the cone of sums of nonnegative circuits (SONC) admits a SOC representation. Based on this, we give a new algorithm for unconstrained polynomial optimization via SOC programming. We also provide a hybrid numeric-symbolic scheme which combines the numerical procedure with a roundingprojection algorithm to obtain exact nonnegativity certificates. Numerical experiments demonstrate the efficiency of our algorithm for polynomials with fairly large degree and number of variables.(c) 2022 Elsevier Ltd. All rights reserved. |
| 资助项目 | Tremplin ERC Stg Grant[ANR-18-ERC2-0004-01] ; FMJH Program PGMO ; EDF ; Thales ; Orange et Criteo ; European Union[813211] ; AI Interdisciplinary Institute ANITI[ANR-19-PI3A-0004] |
| WOS研究方向 | Computer Science ; Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000860188200016 |
| 出版者 | ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60968]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Magron, Victor |
| 作者单位 | 1.CNRS LAAS, 7 Ave colonel Roche, F-31400 Toulouse, France 2.Inst Math, F-31400 Toulouse, France 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Magron, Victor,Wang, Jie. SONC optimization and exact nonnegativity certificates via second-order cone programming[J]. JOURNAL OF SYMBOLIC COMPUTATION,2023,115:346-370. |
| APA | Magron, Victor,&Wang, Jie.(2023).SONC optimization and exact nonnegativity certificates via second-order cone programming.JOURNAL OF SYMBOLIC COMPUTATION,115,346-370. |
| MLA | Magron, Victor,et al."SONC optimization and exact nonnegativity certificates via second-order cone programming".JOURNAL OF SYMBOLIC COMPUTATION 115(2023):346-370. |
入库方式： OAI收割
来源：数学与系统科学研究院
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