From Glossary

Jump to: navigation, search

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,

\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):

1 & 1 & 0 \\
-2 & 0 & 1

Personal tools