Abstract: In this paper, we study a class of Linear Fractional Programming on a nonempty bounded set, called the Problem (LFP), and design a branch and bound algorithm to find the global optimal solution of the problem (LFP). First, we convert the problem (LFP) to the equivalent problem (EP2). Secondly, by applying the linear relaxation technique to the problem (EP2), the linear relaxation programming problem (LRP2_Y ) was obtained. Then, the overall framework of the algorithm is given, and the convergence and complexity of the algorithm are analyzed. Finally, experimental results are listed to illustrate the effectiveness of the algorithm.

Key words: Global optimization, Linear Fractional Programming, Branch and bound algorithm, Linear relaxation