The Global Optimization On The Sum Of Ratios And The Multiplicative

In recent years, with the development of science technique, especially informationtechnique, the applications of global optimization have been wider and wider in fields suchas image processing, chemical engineering design and control, economy design, detabasesand chip design, molecular biology, network engineering, national defence, networks andtransportation, databases and environmental engineering, nuclear and mechanical design,finance and fixed charges. However, distinctive feature of such problems is that they usuallyhave more than one local optimal solution which difer from the global solution. This leadsto that we can not solve the problems easily by classical nonlinear programming techniques.So, studying global optimal solution for this kind of problems has important significanceand challenges extremely. In this paper, we propose a global optimization algorithm fortwo classes of global optimization problems respectively. The main contents are as follows:In Chapter1, we make a brief introduction for some main deterministic approachesand stochastic approaches for solving global optimization problems. Then we give thelatest research development and the brief work is introduced in this article.In Chapter2, we propose a rectangle acceleration algorithm for globally solving thesum of ratios problem (P) with linear constraints. First, with the thought of equivalenttransformation, we convert the problem (P) into an equivalent problem P(RC0). Then,we use the delete rules to delete the parts that do not have optimal solution at the time.Third, with the rectangular subdivision, we subdivide the feasible set. Finally, we construct the convex programming problems of problem P(RC0) and its subproblem at each cuttingdiversity, and then we get the upper bound. Updating the upper and lower bounds, theproblem (P) can be solved. The numerical examples show the efciency of the algorithm.In Chapter3, for the problem (GLMP) with mulplicative objective and linear con-straints,we propose an adaptive bisection algorithm. First, the algorithm make up anequivalent problem (GLMP2). Second, by the interchangeability between objective andconstraint of the auxiliary problem, we convert the key bounding problem to a series ofproblems (Qγ) that can be solved efcently. Third, we solve the problem. Finally, wepresent the convergence analysis and the numerical examples to show the feasibility of theproposed algorithm.