Iterative Algorithm For Generalized Fractional Programming Problems

Generalized fractional programming is one of the most important problems in nonlin-ear optimization problems,and it is widely used in real life,such as,multistage shipping,cluster analysis,bond portfolio,data envelopment analysis and so on.This kind of prob-lem have many local optimal solutions,how to find the global optimal solution attracts many researchers' interest.In recent years,several methods for solving such problem-s have been proposed.In this paper,an iterative algorithm is proposed for a sum of generalized polynomial ratios problem and a class of Minimax fractional programming.Compared with the existing methods of solving these two problems,the algorithm of this paper has a great advantage in both the running time and the feasibility of the optimal solution.The main contents are as follows:In Chapter 1,we first give two kinds of models studied in this paper,then introduce the research background of these two kinds of models and the current relevant researches respectively.Finally,we present the main contents of this paper.In Chapter 2,an iterative algorithm is proposed for the sum of generalized polynomial ratios problem.First of all,by introducing variables,the equivalent problem is obtained.Then,we express each constraint function to equivalent problem as a difference of two polynomials with positive coefficients.And according to the arithmetic-geometric mean inequality,the equivalent problem is reduced to a geometric programming problem.In this way,the optimal solution of original problem can be approximated by solving a series of geometric programming problems.Finally,we give the convergence analysis of the proposed algorithm.Numerical experiments show that the proposed algorithm is feasible and effective.In Chapter 3,we consider a class of Minimax fractional programming problem.First,the original problem is transformed into equivalent problem by introducing variables and exponential transformation.Then the equivalent problem is compressed into convex pro-gramming problem by using the condensed technique in Chapter 2.Therefore,the optimal solution of the original problem is obtained by solving a series of convex programming problems.Finally,the convergence analysis of the algorithm and numerical experiments are given.From the experimental results,it can be seen that the proposed algorithm has some advantages in execution efficiency compared with the existing methods.