Reversed Geometric Programs Treated by Harmonic Means

Abstract

A is a (generalized) polynomial with arbitrary real exponents, but positive coefficients and positive independent variables. Each posynomial program in which a posynomial is to be minimized subject to only inequality posynomial constraints is termed a program. The study of each reversed program is reduced to the study of a corresponding family of (prototype) geometric (namely, posynomial programs in which a posynomial is to be minimized subject to only upper-bound inequality posynomial constraints). This reduction comes from using the classical arithmeticharmonic mean inequality to invert each lower-bound inequality constraint into an equivalent robust family of conservatively approximating upper-bound inequality constraints. The resulting families of programs are then studied with the aid of the *Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213 Partially supported by Research Grant DA-AROD-31-124-71-G17 **Northwestern University, Evanston, Illinois 6O2O1 Partially supported by a Summer Fellowship Grant from Northwestern University. techniques of (prototype) programming. This approach has important computational features not possessed by other approaches, and it can easily be applied to the even larger class of we11-posed algebraic (namely, programs involving real-valued functions that are generated solely by addition, subtraction, multiplication, division, and the extraction of roots).