Global Optimization Study Research On Two Classes Of Multiplicative Programming Problems

Global optimization study is finding the characteristic and calculation method of the the global optimal point on the nonlinear function in a certain area, so it is widely used in economic models, database, image processing and national defense military and other domains etc. Due to the minimum properties of global optimization problem, it’s hard to solve the problem by traditional nonlinear programming method. At present, although the researches on global optimization theory and algorithm have made considerable headway, there are still some problems in algorithm. Based on existing algorithm, this paper puts forward a new and effective algorithm for some special optimization problems.The first chapter states current research methods for global optimization problem: deterministic method and random method, and provides a summary introduction of this paper.In the second chapter, a new accelerating algorithm is presented, which is aimed to solve multiplicative programming problems with index. Firstly, with the aid of equivalent monotone transformation to convert the initiate problem into a optimization problem with the simple variable as objective function and d.m. function as the constraint function. Sec-ondly, find the primal problem’s (ε,η)-optimum solution according to adaptability region segmentation, the solution of auxiliary problem, determination of the lower bound and reducing segmentation. Finally, demonstrate the feasibility and stability of this algorithm from the optimal value of numerical experiments and iterations The third chapter, apply the new accelerating algorithm to solve generalized mul-tiplicative programming problems. Transforming the original problem to the monotone optimization problem, apply adaptability subdivided and reducing segmentation to ap-proach the optimal solution of the original problem. Comparing with other algorithm, this one has improved significantly on optimal solution and iterations, which introduces fewer variables and solves the problems more effectively.