An Adaptive Branch Reduced And Bound Algorithm For Two Classes Of Nonlinear Programming

With the development of science and information technology, the global optimationhas achieved extensive applicatipons in the feld of transportation, economics,computernetwork,physical, chemical and biological.So the theory and algorithm of global optimiza-tion emerge gradually, but not yet very perfect. Especially for the global minimizationproblems, there exist multiple local optimal solutions that difer from the global solution.Thus, it is very difcult to get a global optimal solution for this kind of problems. Inthis paper, for a kind of reverse convex programing and a kind of sum of qurdratic ratiosproblem, we propose a new global optimization method based on existing research. Thethesis is organized as follows:In Chapter1, frst, a brief introduction is given for some classic deterministic ap-proaches and stochastic approaches in order to solve global optimization problems. Thenwe give the latest research development of reverse convex programing and sum of qurdraticratios problem and our work in this paper.In Chapter2, this paper presents an adaptive branch reduced and bound algorithmfor globally solving reverse convex programing (RCP). In order to get an essential optimalsolution of this problem,above all, we transform the problem RCP into an equivalent globalminization problem. Then, by reducing box depend on the auxiliary problem, determiningthe lowwer bound,updating the optimal solution and subdivision,the convergence analysisguarantee that an essential optimal solution is got. Finally, the numerical experiment show the feasibility and efectiveness of the proposed method.In Chapter3, for a class of sum of nonlinear qurdratic ratios problems, we convertoriginal problem into an equivalent monotonic optimization problem where its objectivefunction is increasing and all the constrained functions can be denoted as the diference oftwo increasing functions by introducing some new varibles. Then the algorithm constructsa equivalent problem based on the monotonic characteristic and determines the lowwerbound of the auxiliary problem in order to delete the box. We use an adaptive subdivisionin the branching process at last. The numerical examples report the feasibility and efec-tiveness of the proposed method and the computational efciency is obviously improved inthe list length and the execution time.