A "posynomial" 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 "reversed geometric program". The study of each reversed geometric program is reduced to the study of a corresponding family of approximating (prototype) "geometric programs" (namely, posynomial programs in which a posynomial is to be

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... 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 approximating geometric programs are then studied with the aid of the