Signomial Programming Research Articles

Optimal design of a membrane separation process using signomial programming

A multistage membrane separation process for hydrogen recovery is described and formulated as a signomial programming problem. Two different configurations are examined. A 3-stage and a 5-stage process design problem are solved. The optimal solution to these programs is computed from an initial point that does not satisfy the mass balance or transport constraints of the process, using a primal-based geometric programming code. Also examined is the sensitivity of the optimal solution to changes in purity requirements. In all cases, computation times are very reasonable ranging from 2 to 4 seconds of IBM 370/165 CPU time.

COMPUTATIONAL ASPECTS OF GEOMETRIC PROGRAMMING 3. SOME PRIMAL AND DUAL ALGORITHMS FOR POSYNOMIAL AND SIGNOMIAL GEOMETRIC PROGRAMS

In this paper we consider algorithmic and computational aspects of selected methods for posynomial and signomial programming problems. In particular, we consider the modified concave simplex method for dual posynomial programs and discuss some recent developments suggesting a new dual algorithm. We also consider linear programming based algorithms for primal posynomial programs. Finally, we discuss a recently developed branch and bound method for signomial programming.

One-dimensional problems in unconstrained signomial programming

One-dimensional problems arise in both primal and dual signomial programs. Primal problems are of interest since many multidimensional search procedures involve one-dimensional searches. Dual problems occur naturally since many engineering design problems can be expressed as signomial programs with a single degree of difficulty. This paper applies an interval arithmetic version of Newton's method to one-dimensional unconstrained problems in signomial programming. The interval arithmetic method is guaranteed to generate all the stationary points.

Geometric Programming with Slack Constraints and Degrees of Difficulty

Abstract An algorithm has been developed capable of solving the generalized signomial geometric programming problem, subject to linear or nonlinear constraints of any type, which are either tight or nonbinding at optimality. The algorithm was specifically developed to deal with those problems having degrees of difficulty. Necessary (and sometimes sufficient) conditions for optimality were obtained without increasing the degrees of difficulty in the problem, or using approximation techniques.

Geometric programming with signomials

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).