Geometric Programming

Contrary to popular belief, geometric programming is not just a special technique for studying the very important class of posynomial (optimization) problems. It is really a very general mathematical theory that is especially useful for studying a large class of separable problems. Its practical efficacy is due mainly to the fact that many important (seemingly inseparable) problems can actually be formulated as separable geometric programming problems, by fully exploiting their linear algebraic structure. Some examples are: nonlinear network flow problems (both single-commodity and multicommodity), discrete optimal control problems with linear dynamics, optimal location problems of the generalized Fermat type, (lP constrained) lP regression problems, chemical equilibrium problems, ordinary programming problems, (quadratically constrained) quadratic programming problems, and general algebraic programming problems. The theory of geometric programming includes (i) very strong existence, uniqueness, and characterization theorems, (ii) useful parametric and economic analyses, (iii) illuminating decomposition principles, and (iv) powerful numerical solution techniques. In addition to indicating the true scope of geometric programming and its potential impact on many fields of application, this paper can serve either as a modern introduction to the subject (including an enlightening review of the original posynomial case), or as an up-tate handbook of the most fundamental aspects of the subject.