The Algorithm Of Global Optimization For Solving Generalized Quadratic Programming And Generalized Geometric Programming

In this paper, we mainly study the two kinds of nonconvex programming problemswhich are nonconvex quadratic programming with additional multiplicative constraints andgeneralized geometric programming. They are widely used in the economy, transportation,management and other science. But such problems usually have more than one localoptimal solution, and global optimization method have not a certain criterion in theory totell whether a local optimal solution is the global optimal solution. So it is very difcultto solve the global optimal solution. With the development of the global optimizationmethods, the problem can theoretically be got the approximate feasible solution, within agiven tolerance, which is to be close to the actual optimal solution by the infinite timesof iteration. Unfortunately, for hardest nonconvex problems finding a feasible solutionis almost as difcult as solving the problem itself. Furthermore, if the global optimalsolution happens to be an isolated feasible point, it causes serious dificulties for practicalcomputation. To overcome these limitations, we propose the new method based on thebranch and bound algorithm.The paper is organized as follows:In Chapter1, a brief introduction is given to several deterministic approaches andstochastic approaches. Then we give the latest research development and simply introduceour work in this paper.In Chapter2, we discuss the new global optimization algorithm for the nonconvex quadratic programming with additional multiplicative constraints. Firstly, the originalproblem is equivalent to an monotonic optimization problem whose the objective is asingle variable equation. Secondly, we use adaptive subdivision and construct an auxiliaryproblem to find the (ε, η)-optimal solution. The new global optimization algorithm turnsout that an (ε, η)-optimal solution is adequately guaranteed to be close to the actualoptimal solution. An adaptive subdivison process can be used which may ensure a fasterconvergence than the standard rectangular bisection. Finally, convergence of the algorithmis shown and the experment is given to illustrate the feasibility and efectiveness of thepresent algorithm.In Chapter3, the new global optimization algorithm which is mentioned in chapter2is applied to the generalized geometric programming problem. According to the features ofthe generalized geometric programming problem, it can be transformed into an monotonicoptimization problem. Furthermore, we analyse the key steps about the branch and bound,cut. Compared with other methods, numerical results vindicate that the new algorithm isfeasible.