Treating free variables in generalized geometric global optimization programs

Abstract

Generalized geometric programming (GGP) problems occur frequently in engineering design and management. Recently, some exponential-based decomposition methods [Maranas and Floudas, 1997,Computers and Chemical Engineering 21(4), 351-370; Floudas et al., 1999 , Handbook of Test Problems in Local and Global Optimization, Kluwer Academic Publishers, Boston, pp. 5-105; Floudas, 2000 Deterministic Global Optimizaion: Theory, Methods and Application, Kluwer Academic Publishers, Boston, pp. 257-306] have been developed for GGP problems. These methods can only handle problems with positive variables, and are incapable of solving more general GGP problems. This study proposes a technique for treating free (i.e., positive, zero or negative) variables in GGP problems. Computationally effective convexification rules are also provided for signomial terms with three variables.