Optimization Algorithms For Solving Two Kinds Of Generalized Multiplicative Programming Problems

As a kind of important pptimization problems, nonconvex programming problems can be widely used in the economic and financial, information technology, industrial manu-facturing, and other important fields. Normally, these problems always exist many local optimal solutions which are not the global optimaal solution, so it is very difficult to find their global optimal solutions. Due to nonconvex optimization problems are widely used in the real life, they have attraeted the attention of many researchers in recent years, and some optimization methods have been proposed. This paper proposes the corresponding optimization algorithm for scolving two types of generalized multiplicative programming problems respectively. Compared with existing methods, the proposed branch and bound algorithm and iteration algorithm not only guarantee the quality of the optimal solution but also improve the execution effciency. The main contents are introduced as follows:In Chapter 1, firstly, we put forward optimization model that will be considered in this paper. Secondly,the application background, theoretical significance and current research work of these optiimization models are briefly introduced. Finally, we show the main work of this paper.In Chapter 2. according to the characteristic of generalized linear multiplicative op-timization problem, a new branch and bound algorithm is proposed. First of all. an equivalent problem of the original problem is obtained by introducing new variables.Then, the equivalent problem is transformed into a convex programming problem with the convex relaxation techniques. Next, we get the global optimal solution of the original problem by solving a series of convex programming problems based on a new branching rule. Finally. we prove the global convergence of the algorithm in theory. The results of the numerical experiments declare that the proposed algorithm has some advantage for solving generalized linear multiplicative optimization problem.In Chapter 3, for the generalized polynomial multiplicative optimization problem,an iterative algorithm is presented. Firstly, we get an equivalent generalized geometric programming problem of the original problem by introducing new variables. Secondly,the generalized geometric programming problem is transformed into a standard geometric programming by using arithmetic-geometric average inequality and the idea of penalty function. Thirdly, we obtain the optimal solution of the original optimization problem by solving a series of standard geometric programming problems. In the end,the convergence of the iterative algorithm is given. The results of numerical experiments show that the proposed algorithm is effective and feasible.