Posynomial function

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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.


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.


The function

is a posynomial function, it has the normal representation

The function

is a monomial function, it has the normal representation


  • 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 .