Geometric programming
Authors: Wenjun Zhu(wz274), Sam Olsen(sgo23) (SYSEN5800, FALL 2021)
Introduction
Theory/Methodology
Definition
The standard form of Geometric Programming optimization is to minimize the objective function which must be posynomial. The inequality constraints can only have the form of a posynomial less than or equal to one, and the equality constraints can only have the form of a monomial equal to one.
Standard Form
Minimize $ f_0(x) $
Subject to: $ f_i(x)\leqslant1 $, $ i $ = 1,...,m,
$ g_i(x) = 1 $, $ i $ = 1,...,p,
$ x_i > 0 $, $ i $ = 1,...,q,
where $ f_i(x) $ are posynomial functions, $ g_i(x) $ are monomials, and $ x_i $ are the optimization variables.
Numerical Examples
To solve a standard form Geometric Programming problem
Minimize $ f_0( $
Subject to: $ f_i(x)\leqslant1 $, $ i $ = 1,...,m,
$ g_i(x) = 1 $, $ i $ = 1,...,p,
$ x_i > 0 $, $ i $ = 1,...,q,