Geometric programming

Consider the following posynomial geometric programming problem ... 

Another approach toward the modeling of nonlinear functions of continuous variables is to identify classes of nonlinear functions that can be transformed so as to result in convex nonlinear functions. An important class of nonlinear functions that can be convexified arises in geometric programming and is denoted as posynomials. Posynomials are of the form ... 

Problem (GP) has a nonlinear objective function and nonlinear constraints and, as such, is quite difficult to solve. However, geometric programming problems belong to a class of problems whose dual problems involve only linear constraints. Let be the dual variable associated with the term CillU (Xj) >. Then the dual problem for problem (GP) can be written as follows ... 

For a complete discussion of geometric programming, the interested reader is referred to Duffin et al. (1967), and Beighter and Phillips (1976). Reviews of software for solving geometric programming problems are provided in Dembo (1976) and Rijckaert and Walraven (1985). 

Beightler, C. S., and Phillips, D. T. (1976), Applied Geometric Programming, John WHey Sons, New York. 

Dembo, R. S. (1976), The Current State of the Art of Algorithms and Computer Software for Geometric Programming, Working Paper No. 88, School of Organization and Management, Yale University, New Haven, CT. 

Duffin, R. J., Peterson, E. L., and Zener, C. (1963), Geometric Programming Theory and Application, John WUey Sons, New York. 

Rijckaert, M. J., and Walraven, E. J. C. (1985), Reflections on Geometric Programming, in Computational Mathematical Programming, K. Schittkowski, Ed., Springer, Berlin. 

Geometric conversion factor (interest), 2345 Geometric modeling (CAD), 494 Geometric programming problems (for... 

Templeman, A. B., Structural Design for Minimum Cost using the Method of Geometric Programming , Proc. Instn Civ. Engrs., Vol. 46, Aug. 1970, pp. 459. 

Multi-objective goal programming (MOGoP) Multi-objective geometric programming (MOGeP)... 

W. J. Lee. Determining order quantity and selling price by geometric programming Optimal solution, bounds and sensitivity. Decision Sciences, 24(76-87), 1993. 

---