Study On Global Optimization Algorithm For Generalized Geometric Programming

As a special kind of nonlinear programming, Geometric programming isincreasingly being applied to the practical application, such as finance, chemicalengineering, and electronic engineering and so on. With the increasing of geometricprogramming is applied to the practical application，how to find the solution ofgeometric programming effectively will become very important. In the past twentyyears, there are some good local optimization algorithms for geometric programming,but the global optimization algorithms for geometric programming are less than localoptimization algorithms.This paper mainly studies the global optimization algorithm for generalizedgeometric programming. The new global optimization algorithms for generalizedgeometric programming of this paper are based on the results from home and abroad,and the proposed algorithms are the improvement and extension of previous algorithms.Three algorithms for solving the global optimal solution of generalized geometricprogramming are proposed in this paper.First, based on convex relaxation，we propose a new pruning technique which canbe used to cut away the current investigated region in which the global optimal solutiondoes not exist and improve the convergence speed of the algorithm. With this pruningtechnique, we propose an algorithm for solving the global optimal solution ofgeneralized geometric programming. Convergence of this algorithm is proved, and thenumerical results show that the proposed algorithm is feasible and effective.Second, we propose a global optimization algorithm for generalized geometricprogramming with a new termination condition which can make the algorithm have thefinite termination. Some experiments are reported to show the feasibility of theproposed algorithm.Finally, we present a new relaxation method to get the lower bound of the originalgeneralized geometric programming. We don’t need to solve a convex programming ora linear programming to get the lower bound of the original generalized geometricprogramming, but just need to calculate a formula to get the lower bound of the originalgeneralized geometric programming directly. Adopting this method and combining withthe branch and bound method, we obtain a global optimization algorithm for generalized geometric programming. The algorithm is proved to be convergent, and weprove the algorithm is feasible and effective through some experiments.