A General Alternative Procedure for Solving Negative Degree of Difficulty Problems in Geometric Programming

Authors:
J. L. Alejandre;Ana Allueva;Jose Miguel Gonzalez
Affiliations:
Department of Applied Mathematics, University of Zaragoza, Spain. jlalejan@unizar.es;Department of Applied Mathematics, University of Zaragoza, Spain. allueva@unizar.es;Department of Applied Mathematics, University of Zaragoza, Spain. jgonsan@unizar.es
Venue:
Computational Optimization and Applications
Year:
2004

Citing 1
Cited 1

A new algorithm for geometric programming based on the linear structure of its dual problem

Mathematical and Computer Modelling: An International Journal

A general algorithm for solving Generalized Geometric Programming with nonpositive degree of difficulty

Computational Optimization and Applications

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Abstract

The degree of difficulty is an important concept in classical geometric programming theory. The dual problem is often infeasible when the degree of difficulty is negative and little has been published on this topic. In this paper, an alternative procedure is developed to find the optimal solution for the posynomial geometric programming problem with a negative degree of difficulty. First an equivalent problem was constructed with a positive degree of difficulty and the general posynomial geometric programming problem was solved using an original method previously developed by the authors. This method avoids the difficulty of non-differentiability of the dual objective function in the classical methods classified as dual. It also avoids the problem that appears when the feasible region for the dual problem is formed by an inconsistent system of linear equations.