Outer Space Branch-and-Search Method to Tackle a Class of Linear Fractional Programming Problems and Application in Investment Decision-Making

This paper proposes an outer space branch-and-search method for a class of linear fractional programming problems over a polytope. First, the original problem is reformulated in an equivalent problem by applying the equivalent transformation. Second, by using a new linearization technique, a linear programming relaxation problem of the equivalent problem is constructed. Third, lower bounds are obtained by solving a sequence of linear programming relaxation problems. Fourth, the convergence of the proposed algorithm is proved, and its worst-case computational complexity is estimated. Finally, numerical experimental results are reported to demonstrate the effectiveness of the algorithm. Additionally, an investment decision-making problem was solved to validate the applicability of the method proposed in this paper.