ON A FINITENESS THEOREM ABOUT PROBLEMS INVOLVING INEQUALITIES
WU Wen jun(WU Wen-tsun)
作者信息+
Institute of Systems Science, Academia Sinica, Beijing 100080, China
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ON A FINITENESS THEOREM ABOUT PROBLEMS INVOLVING INEQUALITIES
WU Wen jun(WU Wen-tsun)
Author information+
Institute of Systems Science, Academia Sinica, Beijing 100080, China
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文章历史+
收稿日期
修回日期
出版日期
1900-01-01
1900-01-01
1994-07-15
发布日期
1994-07-15
摘要
Consider the problem of optimizing a polynomial f(X) for X=(x_1,...,x_n) in a closed rectangular-form domain D of the real Euclidean space Rn(X) under constraint polynomial equations HS=0, where HS = {h_1,..,h_r}\subset R[X]. Applying some modified form of Zero Decomposition Theorem to the HS we get in an algorithmic way a finite set of real values K= Keg(f, D, HS) such that the least or greatest value of K is just the least or greatest value of f to be determined. Numerous problems involving inequalities can be settled by means of the above finiteness theorem.
Abstract
Consider the problem of optimizing a polynomial f(X) for X=(x_1,...,x_n) in a closed rectangular-form domain D of the real Euclidean space Rn(X) under constraint polynomial equations HS=0, where HS = {h_1,..,h_r}\subset R[X]. Applying some modified form of Zero Decomposition Theorem to the HS we get in an algorithmic way a finite set of real values K= Keg(f, D, HS) such that the least or greatest value of K is just the least or greatest value of f to be determined. Numerous problems involving inequalities can be settled by means of the above finiteness theorem.
WU Wen jun(WU Wen-tsun). , {{custom_author.name_cn}}.
ON A FINITENESS THEOREM ABOUT PROBLEMS INVOLVING INEQUALITIES. 系统科学与复杂性(英文), 1994, 7(3): 193-200
WU Wen jun(WU Wen-tsun). , {{custom_author.name_en}}.
ON A FINITENESS THEOREM ABOUT PROBLEMS INVOLVING INEQUALITIES. Journal of Systems Science and Complexity, 1994, 7(3): 193-200
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