Contributed Papers

Journal of Optimization Theory and Applications

, Volume 11, Issue 1, pp 3-35

Geometric programming with signomials

  • R. J. DuffinAffiliated withDepartment of Mathematics, Carnegie-Mellon University
  • , E. L. PetersonAffiliated withDepartment of Industrial Engineering and Management Sciences and Department of Mathematics, Northwestern University

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Abstract

The difference of twoposynomials (namely, polynomials with arbitrary real exponents, but positive coefficients and positive independent variables) is termed asignomial.

Each signomial program (in which a signomial is to be either minimized or maximized subject to signomial constraints) is transformed into an equivalent posynomial 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 theequilibrium solutions to thereversed 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-posedalgebraic programs (namely, programs involving real-valued functions that are generated solely by addition, subtraction, multiplication, division, and the extraction of roots).