Many global optimization problems are NP-hard, and require significant specialized knowledge to design appropriate algorithms. The low rank programming problems can also be viewed as global optimization problems, and they have important applications in many fields, especially in management science, finance and investment, system engineering, and so on. In this talk, we consider a class of low rank programming problems, which include some well-known classes of global optimization problems, such as, the sum of linear ratios problems, the multiplicative problems and bilinear programs. An approximation algorithm is presented for solving a class of low rank programming problems with the sum or product of linear ratios objective function, and a new accelerating technique is introduced to improve the computational efficiency of the algorithm. Besides, the rectangular branch-and-bound algorithms with standard bisection rule are shown for solving bilinear programs, the main computational work of the algorithms come down to the solutions of a sequence of linear programming problems, by utilizing the novel linear relaxation techniques. Finally, the numerical experiments are implemented in order to test the performance of these algorithms.