Nonnegative Polynomials and Circuit Polynomials

doi:10.1137/20M1313969

CSpace

	Nonnegative Polynomials and Circuit Polynomials
	Wang, Jie
	2022
发表期刊	SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY
ISSN	2470-6566
卷号	6 期号:2 页码:111-133
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.
关键词	nonnegative polynomial sum of nonnegative circuit polynomials SONC certificate of nonnegativity sum of squares SAGE
DOI	10.1137/20M1313969
收录类别	SCI
语种	英语
资助项目	NSFC[61732001] ; NSFC[61532019]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000788408200002
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60376
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.