查看“︁正项式”︁的源代码

'''正项式'''（英语：posynomial）是一种具有以下形式的函数：

<math>f(x_1, x_2, \dots, x_n) = \sum_{k=1}^K c_k x_1^{a_{1k}} \cdots x_n^{a_{nk}}</math>

其中系数<math>c_k</math>和<math>x_i</math>均为正[[实数]]，指数项<math>a_{ik}</math>为实数。正项式对于加法、数乘和非负的伸缩变换是封闭的。

例如

: <math>f(x_1, x_2, x_3) = 2.7 x_1^2x_2^{-1/3}x_3^{0.7} + 2x_1^{-4}x_3^{2/5}</math>

即為正项式。

正项式和多變數的[[多項式]]不同。多項式的幂次需為非負的整數，但其係數和自變數可以為任意實數。正项式則不同：幂次可以任意實數，但係數和自變數需為正的實數。此名詞是由{{le|Richard Duffin|Richard J. Duffin}}、Elmor L. Peterson和[[克拉倫斯·齊納]]在{{le|幾何規劃|geometric programming}}的書中開始使用的。

正项式是{{le|signomial|signomial}}中的特例，後者沒有限制<math>c_k</math>需為正數。
==參考資料==
*{{cite book
 | author     = Richard J. Duffin
 |author2=Elmor L. Peterson |author3=Clarence Zener
  | title      = Geometric Programming
 | url     = https://archive.org/details/geometricprogram0000unse
 | publisher  = John Wiley and Sons
 | date       = 1967
 | pages      = [https://archive.org/details/geometricprogram0000unse/page/278 278]
 | isbn       = 0-471-22370-0
}}
*{{cite book
 |author       = Stephen P Boyd
 |author2      = Lieven Vandenberghe
 |title        = Convex optimization
 |publisher    = Cambridge University Press
 |date         = 2004
 |isbn         = 0-521-83378-7
 |url          = https://web.stanford.edu/~boyd/cvxbook/
 |access-date  = 2021-04-13
 |archive-date = 2021-12-11
 |archive-url  = https://web.archive.org/web/20211211035846/https://web.stanford.edu/%7Eboyd/cvxbook/
 |dead-url     = no
}}
*{{cite book
 | author      = Harvir Singh Kasana
 |author2=Krishna Dev Kumar
 | title      = Introductory Operations Research: Theory and Applications
 | url      = https://archive.org/details/springer_10.1007-978-3-662-08011-5
 | publisher  = Springer
 | date       = 2004
 | isbn       = 3-540-40138-5 
}}
* {{cite journal | last1 = Weinstock | first1 = D. | last2 = Appelbaum | first2 = J. | title = Optimal solar field design of stationary collectors | journal = Journal of Solar Energy Engineering | volume = 126 | issue = 3| pages = 898–905 | doi = 10.1115/1.1756137 }}

==外部連結==
* S. Boyd, S. J. Kim, L. Vandenberghe, and A. Hassibi, [https://web.archive.org/web/20070308160245/http://www.stanford.edu/~boyd/gp_tutorial.html A Tutorial on Geometric Programming]

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[[Category:函数]]