Geometric Programming: Methods, Computations and Applications

In this paper, we give an applications-oriented survey of geometric programming. This important class of nonlinear programming problems has been intensively studied over the past decade and has played a crucial role in an extremely broad range of applications. The focus of the paper will be on posynomial programs and the slightly more general class of signomial programs. The approach used in studying posynomial programs has been generalized to a much broader class of optimization problems, and an excellent survey of that generalized theory recently appeared in a paper by E. L. Peterson [SIAM Rev., 18 (1976), pp. 1–51]. We do not consider that generalized theory here. It is our intent to provide the reader with an understanding of the basic results in posynomial and signomial programming that have played a crucial role in applications. After reviewing these basic results, we consider computational methods and applications. Three specific applications are considered in detail, and a bibliography indicating the broad range of applications is given.