Nonnegative Polynomials and Circuit Polynomials
文献类型：期刊论文
| 作者 | Wang, Jie |
| 刊名 | SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY
 |
| 出版日期 | 2022 |
| 卷号 | 6期号:2页码:111-133 |
| 关键词 | nonnegative polynomial sum of nonnegative circuit polynomials SONC certificate of nonnegativity sum of squares SAGE |
| ISSN号 | 2470-6566 |
| DOI | 10.1137/20M1313969 |
| 英文摘要 | The concept of sums of nonnegative circuit (SONC) polynomials was recently introduced as a new certificate of nonnegativity especially for sparse polynomials. In this paper, we explore the relationship between nonnegative polynomials and SONCs. As a first result, we provide sufficient conditions for nonnegative polynomials with general Newton polytopes to be a SONC, which generalizes the previous result on nonnegative polynomials with simplex Newton polytopes. Second, we prove that every SONC admits a SONC decomposition without cancellation. In other words, SONC decompositions preserve sparsity of nonnegative polynomials, which is dramatically different from the classical sum of squares decompositions and is a key property to design efficient algorithms for sparse polynomial optimization based on SONC decompositions. |
| 资助项目 | NSFC[61732001] ; NSFC[61532019] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000788408200002 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60375]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Wang, Jie |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China |
| 推荐引用方式 GB/T 7714 | Wang, Jie. Nonnegative Polynomials and Circuit Polynomials[J]. SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY,2022,6(2):111-133. |
| APA | Wang, Jie.(2022).Nonnegative Polynomials and Circuit Polynomials.SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY,6(2),111-133. |
| MLA | Wang, Jie."Nonnegative Polynomials and Circuit Polynomials".SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY 6.2(2022):111-133. |
入库方式： OAI收割
来源：数学与系统科学研究院
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