Book Description

The duality theory of geometric programming as developed by Duffin, Peterson and Zener is based on abstract properties shared by certain classical inequalities, such as Cauchy's arithmetic-geometric mean inequality and Holder's inequality. Inequalities with these abstract properties have been termed 'geometric inequalities.' In this paper we establish a new geometric inequality and use it to extend the 'refined duality theory' for 'posynomial' geometric programs. This extended duality theory treats both 'quadratically-constrained quadratic programs' and 'l sub p-constrained l sub p-approximation (regression) problems' through a rather novel and unified formulation of these two classes of programs. This work generalizes some of the work of others on linearly-constrained quadratic programs, and provides to the best of our knowledge the first explicit formulation of duality for constrained approximation problems. Other people have developed duality theories for a larger class of programs, namely all convex programs, but those theories (when applied to the programs considered here) are not nearly as strong as the theory developed here. This theory has virtually all of the desirable features of its analog for posynomial programs, and its proof provides useful computational procedures. (Author).