A new method for solving the sum of linear and linear fractional programming problems

In this study, an iterative method is suggested for solving the problem in which the objective function is a sum of linear and linear fractional functions, where the constraint functions are in the form of inequalities. The proposed method is based mainly upon the conjugate gradient projection method which is applicable to solve nonlinear programming problems involving linear constraints. The main idea behind this method is to move through the feasible region via a sequence of points in the direction that improves the value of the objective function. Since the earlier methods based on the vertex information may have difficulties as the problem size increases, our method appears to be less sensitive to the problem size. An example is given to clarify the developed theory and the proposed method.