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	Proving inequalities and solving global optimization problems via simplified CAD projection
	Han, Jingjun ; Jin, Zhi ; Xia, Bican
	2015
关键词	CAD projection Global optimization Semi-definiteness Polynomials CYLINDRICAL ALGEBRAIC DECOMPOSITION POLYNOMIAL INEQUALITIES QUANTIFIER ELIMINATION EXISTENTIAL THEORY SETS COEFFICIENTS COMPLEXITY SYSTEMS THEOREM SQUARES
英文摘要	Let x(n) = (x(1),..., x(n)) and f is an element of R[x(n), k]. The problem of finding all k(0) such that f (x(n), k(0)) >= 0 on R-n is considered in this paper, which obviously takes as a special case the problem of computing the global infimum or proving the semi-definiteness of a polynomial. For solving the problems, we propose a simplified Brown-McCallum's CAD projection operator, Nproj, of which the projection scale is always no larger than that of Brown-McCallum's. For many problems, the projection scale is much smaller than that of Brown-McCallum's. As a result, the lifting phase is also simplified. Some new algorithms based on Nproj for solving those problems are designed and proved to be correct. Comparison to some existing tools on some examples is reported to illustrate the effectiveness of our new algorithms. (C) 2015 Elsevier Ltd. All rights reserved.; Peking University; SKLCS project [SYSKF1207]; [NSFC-11290141]; [NSFC-11271034]; SCI(E); ARTICLE; hanjingjunfdfz@gmail.com; j2i5nzhi@sina.com; xbc@math.pku.edu.cn; 206-230; 72
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/20.500.11897/421035]
专题	数学科学学院
推荐引用方式 GB/T 7714	Han, Jingjun,Jin, Zhi,Xia, Bican. Proving inequalities and solving global optimization problems via simplified CAD projection. 2015-01-01.

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