A combination of Broyden-Fletcher-Goldfarb-Shanno (BFGS) and bisection method for solving portfolio optimization problems

In this paper, a new search method known as bisection method is used to obtain the value of objective function and the optimal proportions in a portfolio of six assets in Broyden-Fletcher-Goldfarb-Shanno method. The purpose of this work is to demonstrate how the development of these large-scale optimization methods might help portfolio selection. This research reviews them and shows how they can be implemented in portfolio selection. Based on historical data for six assets, an experimental model is solved with a combination by BFGS and bisection method, as the section of the return interval was reduced by half. The results show that this technique is effective and successful in solving of the portfolio optimization model.