Two Global Optimization Methods For Solving Generalized Geometric Programming

The source of the global optimization problem is quite wide, including finance, produc-tion management, transportation, network engineering, national defence, image processing, chemical engineering design and control, databases and environmental engineering. Dis-tinctive feature of such problems is that they usually have more than one local optimal solution, and these local optimas differ from the global solution. So these problems can not be solved easily by classical nonlinear programming techniques. With the extensive application of global optimization methods, its theories and algorithms have been greatly developed, but these algorithms also have some problems. In this paper, we propose two new methods based on known theories and algorithms for generalized geometric problem.The thesis is organized as follows:In Chapter 1, a brief introduction is given to several mainly deterministic approaches and stochastic approaches. Then we give the latest research development of the generalized geometric program(GGP) and simply introduce our work in this paper.In Chapter 2, this paper presents a new global optimization algorithm for (GGP) problem via a series of single variable equations with unique solution over partitioned sets. Above all, in order to transform (GGP) problem into an equivalent monotonic optimiza-tion problem (P), the proposed approach only introduces one new variable and constraint. Then, by exploiting the monotonic structure of (P) and constructing an auxiliary problem (Q), the solution procedure to (P) is systematically converted into some simple-variable equation problems, which can be easily solved by existing solution methods. This ade-quately guarantees that the proposed algorithm yields an feasible and close to the actual optimal solution. Finally, the numerical experiment is reported to illustrate the feasibility and effectiveness of the proposed method.In Chapter 3, a new algorithm is given for solving (GGP) by the method of solved convex programming. According to the characteristics of the (GGP) problem, it can be converted into a D.C. optimization problem by using the exponential transformation and some other methods, which the objective is a convex function and the constraint functions are D.C. function. Thus, the solution procedure to (GGP) is systematically converted into some convex programming problems by constructing an auxiliary problem. Compared with other methods, numerical results vindicate that the computational efficiency is obviously improved in the list length and the execution time.