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	Open weak CAD and its applications
	Han, Jingjun ; Dai, Liyun ; Hong, Hoon ; Xia, Bican
	2017
关键词	Open weak CAD Open weak delineable CAD projection Semi-definiteness Copositivity CYLINDRICAL ALGEBRAIC DECOMPOSITION QUANTIFIER ELIMINATION COPOSITIVE MATRICES IMPROVED PROJECTION INEQUALITIES COMPLEXITY
英文摘要	The concept of open weak CAD is introduced. Every open CAD is an open weak CAD. On the contrary, an open weak CAD is not necessarily an open CAD. An algorithm for computing projection polynomials of open weak CADs is proposed. The key idea is to compute the intersection of projection factor sets produced by different projection orders. The resulting open weak CAD often has smaller number of sample points than open CADs. The algorithm can be used for computing sample points for all open connected components of f not equal 0 for a given polynomial f. It can also be used for many other applications, such as testing semi-definiteness of polynomials and copositive problems. In fact, we solved several difficult semi-definiteness problems efficiently by using the algorithm. Furthermore, applying the algorithm to copositive problems, we find an explicit expression of the polynomials producing open weak CADs under some conditions, which significantly improves the efficiency of solving copositive problems. (C) 2016 Elsevier Ltd. All rights reserved.; US National Science Foundation Grant [1319632]; National Science Foundation of China [11290141, 11271034, 61532019]; China Scholarship Council; SCI(E); ARTICLE; 785-816; 80
语种	英语
出处	SCI
出版者	JOURNAL OF SYMBOLIC COMPUTATION
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/473866]
专题	数学科学学院
推荐引用方式 GB/T 7714	Han, Jingjun,Dai, Liyun,Hong, Hoon,et al. Open weak CAD and its applications. 2017-01-01.

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