A "signomial" is an algebraic function of one or more independent variables. It is perhaps most easily thought of as an algebraic extension of multi-dimensional polynomials—an extension that permits exponents to be arbitrary real numbers (rather than just non-negative integers) while requiring the independent variables to be strictly positive (so that division by zero and other inappropriate algebraic operations are not encountered).
Formally, let
Then a signomial function has the form
where the coefficients
If we restrict all
For example,
is a signomial.
The term "signomial" was introduced by Richard J. Duffin and Elmor L. Peterson in their seminal joint work on general algebraic optimization—published in the late 1960s and early 1970s. A recent introductory exposition is optimization problems. Although nonlinear optimization problems with constraints and/or objectives defined by signomials are normally harder to solve than those defined by only posynomials (because, unlike posynomials, signomials are not guaranteed to be globally convex), signomial optimization problems often provide a much more accurate mathematical representation of real-world nonlinear optimization problems.