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| A '''posynomial''' is a [[function (mathematics)|function]] of the form
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| : <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>
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| where all the coordinates <math>x_i</math> and coefficients <math>c_k</math> are positive [[real number]]s, and the exponents <math>a_{ik}</math> are real numbers. Posynomials are closed under addition, multiplication, and nonnegative scaling.
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| For example,
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| : <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>
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| is a posynomial. | |
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| Posynomials are not the same as [[polynomial]]s in several independent variables. A polynomial's exponents must be non-negative integers, but its independent variables and coefficients can be arbitrary real numbers; on the other hand, a posynomial's exponents can be arbitrary real numbers, but its independent variables and coefficients must be positive real numbers. This terminology was introduced by [[Richard Duffin|Richard J. Duffin]], Elmor L. Peterson, and [[Clarence Zener]] in their seminal book on [[Geometric programming]].
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| These functions are also known as "'''posinomials'''" in some literature.
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| ==References==
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| *{{cite book
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| | author = Richard J. Duffin
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| | coauthors = Elmor L. Peterson, Clarence Zener
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| | title = Geometric Programming
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| | publisher = John Wiley and Sons
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| | date = 1967
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| | pages = 278
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| | isbn = 0-471-22370-0
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| }}
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| *{{cite book
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| | author = Stephen P Boyd
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| | coauthors = Lieven Vandenberghe
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| | title = Convex optimization ([http://www.stanford.edu/~boyd/cvxbook/ pdf version])
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| | publisher = Cambridge University Press
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| | date = 2004
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| | pages =
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| | isbn = 0-521-83378-7
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| }}
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| *{{cite book
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| | author = Harvir Singh Kasana
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| | coauthors = Krishna Dev Kumar
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| | title = Introductory operations research: theory and applications
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| | publisher = Springer
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| | date = 2004
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| | pages =
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| | isbn = 3-540-40138-5
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| }}
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| * D. Weinstock and J. Appelbaum, "Optimal solar field design of stationary collectors," J. of Solar Energy Engineering, 126(3):898-905, Aug. 2004 http://dx.doi.org/10.1115/1.1756137
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| ==External links==
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| * S. Boyd, S. J. Kim, L. Vandenberghe, and A. Hassibi, [http://www.stanford.edu/~boyd/gp_tutorial.html A Tutorial on Geometric Programming]
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| {{mathapplied-stub}}
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| [[Category:Mathematical optimization]]
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