Posynomial

A posynomial is a function of the form

: $f(x\_1,\; x\_2,\; dots,\; x\_n)\; =\; sum\_\{k=1\}^K\; c\_k\; x\_1^\{a\_\{1k\; cdots\; x\_n^\{a\_\{nk$

where all the coordinates $x\_i$ and coefficients $c\_k$ are positive real numbers, and the exponents $a\_\{ik\}$ are real numbers. Posynomials are closed under addition, multiplication, and nonnegative scaling.

For example,

: $f(x\_1,\; x\_2,\; x\_3)\; =\; 2.7\; x\_1^2x\_2^\{-1/3\}x\_3^\{0.7\}\; +\; 2x\_1^\{-4\}x\_3^\{2/5\}$

is a posynomial.

Posynomials are not the same as polynomials in several variables. A polynomial's coefficients need not be positive, and, on the other hand, the exponents of a posynomial can be real numbers, while for polynomials they must be non-negative integers.

References

*cite book
author = Stephen P Boyd
coauthors = Lieven Vandenberghe
title = Convex optimization ( [http://www.stanford.edu/~boyd/cvxbook/ pdf version] )
publisher = Cambridge University Press
date = 2004
pages =
isbn = 0521833787

*cite book
author = Harvir Singh Kasana
coauthors = Krishna Dev Kumar
title = Introductory operations research: theory and applications
publisher = Springer
date = 2004
pages =
isbn = 3540401385

External links

* S. Boyd, S. J. Kim, L. Vandenberghe, and A. Hassibi, [http://www.stanford.edu/~boyd/gp_tutorial.html A Tutorial on Geometric Programming]