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计算等式约束下多项式在闭长方体上的精确最小值

Computing the equality-constrained minima of polynomial functions in closed hypercuboids
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摘要 对于给定的一个实多项式函数f,多项式环R[x1,…,xn]中一个非空的有限子集H以及Rn中一个闭长方体∏n i=1[ai,bi],给出了一个有效算法,用来计算多项式函数f在集合∏n i=1[ai,bi]∩ZeroR(H)上的精确最小值,这里ZeroR为的实零点集。此外,该算法可产生一个最小值点,该点被写成所谓的区间-有理单元表示。相应的有关算法通过Maple软件被编制成一个通用程序,可处理相关实例。 Let be the field of real numbers, and the ring of polynomials over in variables . For an , a finite subset of and a closed hypercuboid in ,this paper provides an effective algorithm for computing accurately the minimum of in ,where is the set of zeros of in . Moreover, a minimum point can be created by the algorithm in this paper. With the aid of the computer algebraic system Maple,the algorithm has been compiled into a general program to compute the equality-constrained minima of polynomials with rational coefficients.
机构地区 南昌大学数学系
出处 《南昌大学学报(理科版)》 CAS 北大核心 2015年第2期106-114,共9页 Journal of Nanchang University(Natural Science)
基金 国家自然科学基金资助项目(11161034) 江西省自然科学基金资助项目(2015BAB201005)
关键词 多项式函数 等式约束极小化 受约束的最小值 最小值点 吴方法 三角分解 强临界点 修正结式 polynomial function equality-constrained minimization constrained minimum Wu's algorithm triangular decomposition strongly critical point revised resultant
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