A new rectangle branch-and-pruning approach for generalized geometric programming

Generalized geometric programming (GGP) problem occurs frequently in engineering design and management. In this paper, a branch-and-pruning global optimization algorithm is proposed for GGP. By utilizing some transformations, a linear relaxation of the problem (GGP) is obtained based on the linear lower bound functions of objective and constraint functions inside some hyperrectangle region. Then a new pruning technique is given to accelerate the convergence of the given algorithm, and this pruning technique offers the possibility to cut away a large part of the current investigated region in which there no exist global optimum solution. The proposed algorithm which connects branch-and-bound method with the pruning technique successfully is convergent to the global minimum, according to the successive refinement of the linear relaxation of feasible region of the objective function and the solutions of a series of linear relaxation problems. And finally numerical experiment is given to illustrate the feasibility and efficiency of the proposed algorithm.