Geometric Programming with Signomials

The difference of two posynomials (namely, polynomials with arbitrary real exponents, but positive coefficients and positive independent variables) is termed a signomial. Each signomial program (in which a signomiat is to be either minimized or maximized subject to signomial constraints) is transformed into an equivalent posynomiat program in which a posynomial is to be minimized subject only to inequality posynomial constraints. The resulting class of posynomial programs is substantially larger than the class of (prototype) geometric programs (namely, posynomial programs in which a posynomial is to be minimized subject only to upper- bound inequality posynomial constraints). However, much of the (prototype) geometric programming theory is generalized by studying the equilibrium solutions to the reversed geometric programs in this larger class. Actually, some of this theory is new even when specialized to the class of prototype geometric programs. On the other hand, all of it can indirectly, but easily, be applied to the much larger class of well- posed algebraic programs (namely, programs involving real- valued functions that are generated solely" by addition, subtraction, multiplication, division, and the extraction of roots).