Linearization method of global optimization for generalized geometric programming

Many methods for solving generalized geometric programming (GGP) problem can only find locally optimal solutions. But up to now, less work has been devoted to solving global optimization of GGP due to the inherent difficulty. This paper gives a method for finding the globally optimal solutions of GGP. Utilizing an exponentially variable transformation and some other techniques the initial nonlinear and nonconvex GGP problem is reduced to a sequence of linear programming problems. The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Several GGP examples in the literatures are tested to demonstrate that the proposed method can systematically solve these examples to find the global optimum within a prespecified error.