# Posynomial function

A *posynomial ***function** (also written as a *posinomial ***function** ) and the **monomial** function closely related to it are functions that are used in the formulation of geometric programs . They can be seen as generalizations of polynomial functions in several variables, since any real exponents are allowed.

## definition

Be for as well as for . Then the function is called

a posynomial function. Everyone is there . If the sum consists of only one sum term, one speaks of a monomial function.

## example

The function

is a posynomial function, it has the normal representation

The function

is a monomial function, it has the normal representation

## properties

- Posynomial functions are closed under addition, multiplication and multiplication with positive scalars.
- Monomial functions are completed under multiplication, division and positive scaling.
- The posynomial functions thus in particular form a convex cone in the vector space of all functions , the monomial functions at least a (dotted) linear sub- cone .

## literature

- Boyd, Stephen; Vandenberghe, Lieven (2004). Convex Optimization. Cambridge University Press. ISBN 978-0-521-83378-3 . ( online )