Engineering Optimization, 5th Edition

8 Geometric Programming

8.1 Introduction

Geometric programming is a relatively new method of solving a class of nonlinear programming problems compared to general NLP. It was developed by Duffin et al [1]. It is used to minimize functions that are in the form of posynomials subject to constraints of the same type. It differs from other optimization techniques in the emphasis it places on the relative magnitudes of the terms of the objective function rather than the variables. Instead of finding optimal values of the design variables first, geometric programming first finds the optimal value of the objective function. This feature is especially advantageous in situations where the optimal value of the objective function may be all that is of interest. In such cases, calculation of the optimum design vectors can be omitted. Another advantage of geometric programming is that it often reduces a complicated optimization problem to one involving a set of simultaneous linear algebraic equations. The major disadvantage of the method is that it requires the objective function and the constraints in the form of posynomials. We will first see the general form of a posynomial.

8.2 Posynomial

In an engineering design situation, frequently the objective function (e.g. the total cost) f (X) is given by the sum of several component costs U _i (X) as

(8.1)

In many cases, the component ...