Solving Fractional Geometric Programming Problems via Relaxation approach

In the optimization literature , Geometric Programming problems play a very important role rather than primary in engineering designs. The geometric programming problem is a nonconvex optimization problem that has received the attention of many researchers in the recent decades. Our main focus in this issue is to solve a Fractional Geometric Programming(FGP) problem via linearization technique[1]. Linearizing separately both the numerator and denominator of the fractional geometric programming problem in the objective function, causes the problem to be reduced to a Fractional Linear Programming problem (FLPP) and then the transformed linearized FGP is solved by Charnes and Cooper method which in fact gives a lower bound solution to the problem. To illustrate the accuracy of the final solution in this approach, we will compar our result with the LINGO software solution of the initial FGP problem and we shall see a close solution to the globally optimum. A numerical example is given in the end to illustrate the methodology and efficiency of the proposed approach

Global Optimization for the Sum of Concave-Convex Ratios Problem

This paper presents a branch and bound algorithm for globally solving the sum of concave-convex ratios problem (P) over a compact convex set. Firstly, the problem (P) is converted to an equivalent problem (P1). Then, the initial nonconvex programming problem is reduced to a sequence of convex programming problems by utilizing linearization technique. The proposed algorithm is convergent to a global optimal solution by means of the subsequent solutions of a series of convex programming problems. Some examples are given to illustrate the feasibility of the proposed algorithm