A Class Of Global Convergence Algorithm For Nonlinear Programming

Optimization is a highly application academic, it has a wild range of applications in the economic field, engineering,management, but with the deepening of researching and practical problems demand, the precision that we solve the optimal values demand high increasingly, therefore, the global optimization problem is more concern than before, it has become an important branch in recent decades, at the same time, a global optimization problem carry multiple local optimal solution, which makes the solution of this problem become very challenging.In this paper, some geometric programming algorithm for global optimization conducted indepth research, and proposes a new and more practical algorithms- -—branch and bound algorithm, the main work consists of the following three aspects:First, the special form for the geometric programming—definite geometric programming problem, above of all, through the equivalent transformation, the original problem into the equivalent problem, then the equivalent problem is done a series of transformations and estimated the lower bound of it. The original problem is turned into the linear programming relaxation, and finally the solution of these linear programming relaxation are solved, the solutions approach to the optimal solution, and prove its convergence theoretically.Second, generalized geometric programming problem with box-type constraints, we take full advantage of the characteristics of geometric programming, transform it into a linear programming relaxation, take use of the new branch and bound algorithm and obtain its global optimal solution, and proved its convergence.Third, the non-convex polynomial programming problem with rational indices, through two relaxation methods we turn it into the relaxation of the linear programming problem with integer index, and the combination of variables makes the problem appear easier to solve and improve the efficiency of computer operations, and reduce the number of iterations, at the same time,the using of branch and bound algorithm to solve a series of linear programming relaxation, and finally the solution to approximate the solution of the original optimal problem, and prove its feasibility theoretically.