A Global Optimization Method for Nonlinear Fractional Programs

Abstract

Despite extensive research has been undertaken on global optimization during the late 20(superscript th) century, global optimization methods have not often been applied to fractional programming, especially for nonlinear fractional programs owing to its complexity. Since management activities frequently desire to optimize certain indicators in various proportions, such as financial planning (debt/equity ratio), production planning (output/employee ratio), etc., many decisional models have been considered as fractional programs. Accordingly, linear fractional programming has been widely applied in numerous management problems due to its simplicity. However, linear fractional programming cannot describe all real-life problems, and unfortunately a nonlinear fractional program describes most practical problems significantly better than a linear fractional program does. Therefore, this study aims to develop a global optimization method for solving nonlinear fractional programming problems.