Posynomial

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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}


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