Iterative Algorithms For Two Types Of Fractional Programming Problems

The fractional programming problem is an important class of non-convex optimization problems,and it is widely applied in real life,such as,quadratic assignment problem,traffic design,project management,communication system,scale economy,etc.These problems usually have multiple local optimal solutions,which are difficult to solve globally,so they have attracted the attention of many scholars.In recent years,many algorithms have been proposed to solve the problems,such as,branch and bound algorithm,simplexlike sequential method and parametric approach.In this thesis,for a class of quadratically constrained sum of quadratic ratios and a sum of generalized polynomial ratios problem,the iterative algorithms are given respectively.The main contents are as follows:In Chapter 1,we give two classes of problems studied in this thesis,and then introduce the research background,theoretical significance and the current relevant researches of these two kinds of models respectively.Finally,we present the main contents of this thesis.In Chapter 2,an iterative algorithm is proposed for the sum of quadratic ratios fractional programming problem.First of all,by introducing variables,the equivalent form of the problem is obtained.Then,by introducing signs and transforming,we express each constraint function to equivalent problem as the ratio of two polynomials with positive coefficients.Next,by using the compression method,the equivalent problem is converted into a geometric programming problem.In this way,the solution of the original problem can be obtained by solving a series of geometric programming problems.In the end,the convergence of the algorithm is given.Numerical results illustrate the feasibility and efficiency of the proposed algorithm.In Chapter 3,we consider a class of sum of generalized polynomial ratios fractional programming problem.First,the original problem is transformed into its equivalent problem by exponential transformation and introducing variables,then the equivalent problem is converted into a convex programming problem by utilizing convexification method.By solving a sequence of convex programming problems,we can obtain the optimal solution of the problem.Finally,we give the convergence analysis of the algorithm.And the numerical results show that the algorithm is feasible and effective.