| 书目名称 | Nondifferentiable Optimization and Polynomial Problems | | 编辑 | Naum Z. Shor | | 视频video | | | 丛书名称 | Nonconvex Optimization and Its Applications | | 图书封面 |  | | 描述 | Polynomial extremal problems (PEP) constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. Let :e = {:e 1, ... , :en} be the vector in n-dimensional real linear space Rn; n PO(:e), PI (:e), ... , Pm (:e) are polynomial functions in R with real coefficients. In general, a PEP can be formulated in the following form: (0.1) find r = inf Po(:e) subject to constraints (0.2) Pi (:e) =0, i=l, ... ,m (a constraint in the form of inequality can be written in the form of equality by introducing a new variable: for example, P( x) ~ 0 is equivalent to P(:e) + y2 = 0). Boolean and mixed polynomial problems can be written in usual form by adding for each boolean variable z the equality: Z2 - Z = O. Let a = {al, ... ,a } be integer vector with nonnegative entries {a;}f=l. n Denote by R[a](:e) monomial in n variables of the form: n R[a](:e) = IT :ef‘; ;=1 d(a) = 2:7=1 ai is the total degree of monomial R[a]. Each polynomial in n variables can be written as sum of monomials with nonzero coefficients: P(:e) = L caR[a](:e), aEA{P) IX x | | 出版日期 | Book 1998 | | 关键词 | Mathematica; algebra; algorithms; calculus; complexity; graph theory; optimization; programming; combinatori | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4757-6015-6 | | isbn_softcover | 978-1-4419-4792-5 | | isbn_ebook | 978-1-4757-6015-6Series ISSN 1571-568X | | issn_series | 1571-568X | | copyright | Springer Science+Business Media Dordrecht 1998 |
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发表于 2025-3-21 19:47:01
