Robustness of Posynomial Geometric Programming Optima

This paper develops a simple bounding procedure for the optimal value of a posynomial geometric programming (GP) problem when some of the coefficients for terms in the problem's objective function are estimated with error. The bound may be computed even before the problem is solved and it is shown analytically that the optimum value is very insensitive to errors in the coefficients; for example, a 20% error could cause the optimum to be wrong by no more than 1.67%. Key Words: Geometric Programming, Posynomials, Sensitivity Analysis *Corresponding Author Address: Department of Industrial Engineering 1048 Benedum Hall University of Pittsburgh Pittsburgh, PA 15261 e-mail: rajgopal@engrng.pitt.edu fax: (412) 624-9831 1 Introduction Geometric Programming (GP) is a technique for solving certain classes of algebraic nonlinear optimization problems. Since its original development by Duffin, Peterson and Zener (1967) at the Westinghouse R & D Center, it has been studied extensively and..