# Posynomial

A positive sum of monomials: $LaTeX: \textstyle \sum_i c(i) \prod_{j} [x(j)^{a(i,j)}],$ where $LaTeX: c > 0.$ Each monomial is the product,

$LaTeX: \prod_j [x(j)^{a(i,j)}] = x(1)^{a(i,1)} \times x(2)^{a(i,2)} \times \dots \times x(n)^{a(i,n)},$

and $LaTeX: [a(i, j)]$ is called the exponent matrix. This is the fundamental function in geometric programming.

Example: $LaTeX: \textstyle x(1)x(2) + 2x(3)/x(1)^{2}$ is a posynomial with 2 monomial terms and 3 variables. The exponent matrix is 2 by 3, showing the exponent in each monomial (row) of each variable (column):

$LaTeX: \begin{bmatrix} 1 & 1 & 0 \\ -2 & 0 & 1 \end{bmatrix}$