ABSTRACT
In geometric programming, the objective function is written in posynomial form:
f cx x x xa a a n an( )x = …1 2 31 2 3 (8.1)
where c is a positive constant, the exponents ai are real numbers, and xi are the design variables that can take positive values. It is important to note that in polynomials, c can take both positive and negative values. For example,
f x x x x( )x = − −5 2 31 2
is a polynomial, while
f x x x x( )x = + + − −2 5 41 2
is a posynomial. If the objective function is obtained in polynomial form, then it has to be
transformed into a posynomial before geometric programming techniques can be used. For example, the maximization function f x x( )x = 1
transformed into a posynomial form minimization function f x x( )x = − −1 2
It is very interesting to note that in geometric programming, the objective function is evaluated first and then optimal design variables are obtained. That is, the optimized value of the objective function can be obtained without knowing the optimal value of design variables. Thus, the solution to geometric programming problems does not depend on the initial guess. In this chapter, both unconstrained and constrained optimization problems are solved using geometric programming. The chapter concludes with a practical application of geometric programming. The road map for this chapter is given in Figure 8.1.
