Nonnegative Polynomials and Circuit Polynomials

doi:10.1137/20M1313969

	Nonnegative Polynomials and Circuit Polynomials
	Wang, Jie
刊名	SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY
	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
出版者	SIAM PUBLICATIONS
WOS记录号	WOS:000788408200002
内容类型	期刊论文
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.